arXiv subjects

A. J. M. Medved

Publications and source records attributed to A. J. M. Medved.

At least 19 recordsLinked to original sources

arXiv2026

Defrosting the Born-Infeld dyonic frozen star with tachyon matter: spectrum of oscillations

The frozen star is a model for the interior of an astrophysical black hole that is externally indistinguishable from the singular geometry of a Schwarzschild black hole, even though it contains no singularities nor trapped surfaces. The frozen star corresponds to a macroscopic ``BIon'', a solution of a certain type of Born-Infeld Lagrangian coupled to Einstein gravity, which consists of rigid flux tubes sourced by an electric charge localized at its center and a uniform distribution of opposite charge along its outer surface. This configuration is a solution of the effective action that describes the end point of tachyon condensation in string. The rigidity of the flux tubes implies that the star is ultrastable under linear perturbations of the geometry and matter. The star can be effectively deformed, or ``defrosted'', allowing internal pulsations, as expected from regular, horizonless astrophysical black holes. To describe the defrosted star, we need to include a perturbative amount of magnetic-monopole charge and tachyon kinetic energy. This recasts the star as a macroscopic ``DIon'', whose flux tubes can stretch and contract, having both electric and magnetic charges localized at its center and distributed uniformly along its outer surface. Previously, the non-radial oscillations of the defrosted star were analyzed to leading order in a perturbative ``defrosting'' parameter $γ$, by describing the energy-momentum tensor as that of a fluid. Here, we derive the same spectrum in a much simpler way, using the Born-Infeld Lagrangian. Thus, we verify that the sound velocities scale as $γ$ and the parametrically long lifetimes scale as $1/γ^2$. Because the perturbation equations are derived from a Lagrangian, their consistency is guaranteed for arbitrary deviations away from spherical symmetry, facilitating numerical studies on frozen stars away from equilibrium.

gr-qc↗

arXiv2026

Quantum gravitational effects suppress the formation of trapped surfaces

Classical general relativity predicts that a contracting, spherically symmetric matter system with a large-enough mass will result in the formation of a trapped region whose outer boundary is an apparent horizon where the gravitational redshift diverges. The incompleteness theorems then lead to the conclusion that the outcome of the collapse is the singular geometry of a Schwarzschild black hole. Both analyses rely on solving Einstein's equations, a set of partial differential equations, valid in the limit that the Schwarzschild radius is finite but the Planck length is set to zero, so that quantum fluctuations of the geometry are completely absent. Here, we keep both parameters finite, allowing the geometry to fluctuate quantum mechanically, and take the limit of vanishing Planck length only at the end. Expressing the geometry of a spherically symmetric, collapsing, thin shell of matter in terms of an effective quantum field theory in 1+1 dimensions, we show, using the standard techniques of quantum field theory in curved spacetime, that the production of particles as the shell approaches its would-be horizon is finite in the limit of vanishing Planck length. The total number of produced quanta of the gravitational field scales as the Bekenstein-Hawking entropy, while their total energy scales as the mass of the shell. Importantly, the quantum expectation value of the product of the scalar expansion parameters for the associated null vectors is never vanishing. The conclusion is that an apparent horizon is not formed even when the shell has reached its gravitational radius. As the collapse continues, the classical Schwarzschild geometry can no longer be used to describe the shell's exterior geometry. This provides the sought-after loophole that is needed to explain how astrophysical black holes could be compact objects that are regular and horizonless.

gr-qc↗

arXiv2025

Formation of Frozen Stars from collapsing matter by tunneling

The frozen star is a type of black hole mimicker: An ultracompact object whose exterior geometry resembles that of a general-relativistic black hole but differs in its matter composition and in the regularity of its interior geometry. It is sourced by a spherically symmetric collection of open-string flux tubes, which posses an extremely anisotropic energy-momentum-stress tensor with maximally negative radial pressure. The frozen star represents an effective classical description of the highly quantum, closed-string polymer model. A key challenge for any model of a black hole mimicker is to explain how such objects can form from a collapsing body of matter. We started to address this important problem in a previous article by adapting the Euclidean-action method of Gibbons and Hawking to show that the transition into a frozen star is likely. Here, we improve on our previous results by showing that the transition probability for a collapsing shell of matter to tunnel quantum mechanically into a frozen star is unity, up to negligible corrections. Our conclusion is that such a transition is therefore inevitable.

gr-qc↗

arXiv2024

Defrosting frozen stars: spectrum of non-radial oscillations

The frozen star model describes a type of black hole mimicker; that is, a regular, horizonless, ultracompact object that behaves just like a Schwarzschild black hole from an external-observer's perspective. In particular, the frozen star is bald, meaning that it cannot be excited. To mimic the possible excitations of the frozen star, it needs to be "defrosted" by allowing deviations from the maximally negative radial pressure and vanishing tangential pressure of the fluid sourcing the star. Here, we extend a previous study on non-radial oscillations of the defrosted star by considering, in addition to the fluid modes, the even-parity metric perturbations and their coupling to the fluid modes. At first, general equations are obtained for the perturbations of the energy density and pressure along with the even-parity perturbations of the metric for a static, spherically symmetric but otherwise generic background with an anisotropic fluid. This formal framework is then applied to the case of a defrosted star. The spectrum of non-radial oscillations is obtained to leading order in an expansion in terms of $γ$, which is the small relative deviation away from maximally negative radial pressure. We find that the sound velocity of the modes is non-relativistic, and proportional to $γ$, while their lifetime is parametrically long, proportional to $1/γ^2$. This result was anticipated by previous discussions on the collapsed polymer model, whose strongly non-classical interior is argued to provide a microscopic description of the frozen and defrosted star geometries. Our results will serve as a starting point for calculating the spectrum of emitted gravitational waves from an excited frozen star.

gr-qc↗

arXiv2024

Kerr Black hole mimickers sourced by a string fluid

We present rotating solutions of Einstein's gravity coupled to an effective Born-Infeld theory that describes the end of open-string tachyon condensation after the decay of an unstable $D$-brane or a brane-antibrane system. The geometry of these solutions is that of the rotating frozen star. The solutions are stationary, non-singular and ultracompact, and their exterior geometry is identical, for all practical purposes, to that of the Kerr solution. The Born-Infeld matter consists of radial electric-flux tubes that emanate from, or end at, the ellipsoidal core of the star. Each end of the flux tubes carries an electric charge, so that the electric field can be viewed as being sourced by an ellipsoidal charge distribution of positive and negative charges near the center of the star. Meanwhile, the star's outer layer is equal and oppositely charged, resulting in a vanishing electric field in the external spacetime. We show that these rotating solutions are ultrastable against radial perturbations, just like their static frozen star counterparts. They are also effectively immune to ergoregion instabilities, as we discuss.

hep-th↗

arXiv2024

Frozen stars: Black hole mimickers sourced by a string fluid

The frozen star is a non-singular, ultracompact object that, to an external observer, looks exactly like a Schwarzschild black hole, but with a different interior geometry and matter composition. The frozen star needs to be sourced by an extremely anisotropic fluid, for which the sum of the radial pressure and energy density is either vanishing or perturbatively small. Here, we show that this matter can be identified with the string fluid resulting from the decay of an unstable $D$-brane or a brane-antibrane system at the end of open-string tachyon condensation. The string fluid corresponds to flux tubes emanating from the center and ending at the Schwarzschild radius of the star. The effective Lagrangian for this fluid can be recast into a Born-Infeld form. When the fluid Lagrangian is coupled to that of Einstein's Gravity, the static, spherically symmetric solutions of the equations of motion are shown to be the same as those describing the frozen star model. Frozen stars can therefore be viewed as gravitationally back-reacted BIons. The Born-Infeld Lagrangian provides a complete set of equations that describe the dynamics of the frozen star in a generic state, which is not necessarily static nor spherically symmetric. Additionally, this description provides a new physical perspective on the structure of the frozen star in terms of the corresponding electric fields and charges. The electric field is sourced by a point-like charge at the center of the star, while its outer layer is equal and oppositely charged. The electric force between the charges is offset because the mass of the star is fixed.

hep-th↗

arXiv2023

Sourcing the Kerr geometry

The Kerr metric is a vacuum solution of the Einstein equations outside of a rotating black hole, but what interior matter is actually rotating and sourcing the Kerr geometry? Here, we describe a rotating exotic matter which can source the Kerr geometry for the entire acceptable range of its spin parameter and be shown to saturate the radial null-energy condition at every point in the interior, while being free of any obvious pathologies. We do so by introducing the rotating frozen star, whose compactness is controlled by a perturbative parameter and whose outer surface can be arbitrarily close to the horizon of a Kerr black hole. The interior geometry modifies Kerr's such that there is neither an inner ergosphere nor an inner horizon, and the metric and Einstein tensors are regular everywhere except for a mild, removable singularity at the center of the star. The geometry of each radial slice of the interior is a nearly null surface with the same geometry, but different radial size, as that of the would-be horizon on the outermost slice. Moreover, the metric limits to that of the static frozen star as the spin is taken to zero. The integral of the energy density leads to a rest mass that is equal to the irreducible mass of a Kerr black hole, and the integral of the angular-momentum density confirms that the ratio of the angular momentum to the mass is equal to the Kerr spin parameter. Including the rotational energy in the standard way, we then obtain the total gravitational mass and angular momentum of a Kerr black hole with the same mass and spin parameters. We propose that the rotating frozen star provides a classical description of the highly quantum final state of gravitationally collapsed matter, which features a maximally entropic, stringy fluid as described by our polymer model for the black hole interior.

gr-qc↗

arXiv2023

Thermodynamics of frozen stars

The frozen star is a recent proposal for a non-singular solution of Einstein's equations that describes an ultracompact object which closely resembles a black hole from an external perspective. The frozen star is also meant to be an alternative, classical description of an earlier proposal, the highly quantum polymer model. Here, we show that the thermodynamic properties of frozen stars closely resemble those of black holes: Frozen stars radiate thermally, with a temperature and an entropy that are perturbatively close to those of black holes of the same mass. Their entropy is calculated using the Euclidean-action method of Gibbons and Hawking. We then discuss their dynamical formation by estimating the probability for a collapsing shell of "normal" matter to transition, quantum mechanically, into a frozen star. This calculation followed from a reinterpretation of a transitional region between the Euclidean frozen star and its Schwarzschild exterior as a Euclidean instanton that mediates a phase transition from the Minkowski interior of an incipient Schwarzschild black hole to a microstate of the frozen star interior. It is shown that, up to negligible corrections, the probability of this transition is $e^{-A/4}$, with $A$ being the star's surface area. Taking into account that the dimension of the phase space is $e^{+A/4}$, we conclude that the total probability for the formation of the frozen star is of order unity. The duration of this transition is estimated, which we then use to argue, relying on an analogy to previous results, about the scaling of the magnitude of the off-diagonal corrections to the number operator for the Hawking-like particles. Such scaling was shown to imply that the corresponding Page curve indeed starts to go down at about the Page time, as required by unitarity.

gr-qc↗

arXiv2023

Defrosting frozen stars: spectrum of internal fluid modes

The frozen star model provides a classical description of a regularized black hole and is based upon the idea that regularizing the singularity requires deviations from the Schwarzschild geometry which extend over horizon-sized scales, as well as maximally negative radial pressure as an equation of state. The frozen star has also been shown to be ultra-stable against perturbations; a feature that can be attributed to the equation of state and corresponds to this model mimicking a black hole in the limit $\hbar\to 0$ or, equivalently, the limit of infinite Newton's constant. Here, we ``defrost'' the frozen star by allowing its radial pressure to be perturbatively less negative than maximal. This modification to the equation of state is implemented by appropriately deforming the background metric so as to allow the frozen star to mimic a quantum black hole at finite $\hbar$ and Newton's constant. As a consequence, the defrosted star acquires a non-trivial spectrum of oscillatory perturbations. To show this, we first use the Cowling approximation to obtain generic equations for the energy density and pressure perturbations of a static, spherically symmetric background with an anisotropic fluid. The particular setting of a deformed frozen star is then considered, for which the dispersion relation is obtained to leading order in terms of the deviation from maximal pressure. The current results compare favorably with those obtained earlier for the collapsed polymer model, whose strongly non-classical interior is argued to provide a microscopic description of the frozen and defrosted star geometries.

gr-qc↗

arXiv2023

Black holes as frozen stars: Regular interior geometry

We have proposed a model geometry for the interior of a regular black hole mimicker, the frozen star, whose most startling feature is that each spherical shell in its interior is a surface of infinite redshift. The geometry is a solution of the Einstein equations which is sourced by an exotic matter with maximally negative radial pressure. The frozen star geometry was previously presented in singular coordinates for which $-g_{tt}$ and $g^{rr}$ vanish in the bulk and connect smoothly to the Schwarzschild exterior. Additionally, the geometry was mildly singular in the center of the star. Here, we present regular coordinates for the entirety of the frozen star. Each zero in the metric is replaced with a small, dimensionless parameter $\varepsilon$; the same parameter in both $-g_{tt}$ and $g^{rr}$ so as to maintain maximally negative radial pressure. We also regularize the geometry, energy density and pressure in the center of the star in a smooth way. Our initial analysis uses Schwarzschild-like coordinates and applies the Killing equations to show that an infalling, point-like object will move very slowly, effectively sticking to the surface of the star and never coming out. If one nevertheless follows the trajectory of the object into the interior of the star, it moves along an almost-radial trajectory until it comes within a small distance from the star's center. Once there, if the object has any amount of angular momentum at all, it will be reflected outwards by a potential barrier onto a different almost-radial trajectory. Finally, using Kruskal-like coordinates, we consider the causal structure of the regularized frozen star and discuss its $\varepsilon\to 0$ limit, for which the geometry degenerates and becomes effectively two dimensional.

gr-qc↗

arXiv2021

Black holes as frozen stars

We have recently proposed a model for a regular black hole, or an ultra-compact object, that is premised on having maximally negative radial pressure throughout the entirety of the object's interior. This model can be viewed as that of a highly entropic configuration of fundamental, closed strings near the Hagedorn temperature, but from the perspective of an observer who is ignorant about the role of quantum physics in counteracting against gravitational collapse. The advantage of this classical perspective is that one can use Einstein's equations to define a classical geometry and investigate its stability. Here, we complete the model by studying an important aspect of this framework that has so far been overlooked: The geometry and composition of the outermost layer of the ultra-compact object, which interpolates between the bulk geometry of the object and the standard Schwarzschild vacuum solution in its exterior region. By imposing a well-defined set of matching conditions, we find a metric that describes this transitional layer and show that it satisfies all the basic requirements; including the stability of the object when subjected to small perturbations about the background solution. In fact, we are able to show that, at linearized order, all geometrical and matter fluctuations are perfectly frozen in the transitional layer, just as they are known to be in the bulk of the object's interior.

gr-qc↗

arXiv2020

A correspondence between strings in the Hagedorn phase and asymptotically de Sitter space

A correspondence between closed strings in their high-temperature Hagedorn phase and asymptotically de Sitter (dS) space is established. We identify a thermal, conformal field theory (CFT) whose partition function is, on the one hand, equal to the partition function of closed, interacting, fundamental strings in their Hagedorn phase yet is, on the other hand, also equal to the Hartle-Hawking (HH) wavefunction of an asymptotically dS Universe. The Lagrangian of the CFT is a functional of a single scalar field, the condensate of a thermal scalar, which is proportional to the entropy density of the strings. The correspondence has some aspects in common with the anti-de Sitter/CFT correspondence, as well as with some of its proposed analytic continuations to a dS/CFT correspondence, but it also has some important conceptual and technical differences. The equilibrium state of the CFT is one of maximal pressure and entropy, and it is at a temperature that is above but parametrically close to the Hagedorn temperature. The CFT is valid beyond the regime of semiclassical gravity and thus defines the initial quantum state of the dS Universe in a way that replaces and supersedes the HH wavefunction. Two-point correlation functions of the CFT scalar field are used to calculate the spectra of the corresponding metric perturbations in the asymptotically dS Universe and, hence, cosmological observables in the post-inflationary epoch. Similarly, higher-point correlation functions in the CFT should lead to more complicated cosmological observables.

hep-th↗

arXiv2019

Lower limit on the entropy of black holes as inferred from gravitational wave observations

Black hole (BH) thermodynamics was established by Bekenstein and Hawking, who made abstract theoretical arguments about the second law of thermodynamics and quantum theory in curved spacetime respectively. Testing these ideas experimentally has, so far, been impractical because the putative flux of Hawking radiation from astrophysical BHs is too small to be distinguished from the rest of the hot environment. Here, it is proposed that the spectrum of emitted gravitational waves (GWs) after the merger of two BHs, in particular the spectrum of GW150914, can be used to infer a lower limit on the magnitude of the entropy of the post-merger BH. This lower bound is potentially significant as it could be of the same order as the Bekenstein-Hawking entropy. To infer this limit, we first assume that the result of the merger is an ultracompact object with an external geometry which is Schwarzschild or Kerr, but with an outer surface which is capable of reflecting in-falling GWs rather than fully absorbing them. If the absence of deviations from the predictions of general relativity in detected GW signals will be verified, we will then obtain a bound on the minimal redshift factor of GWs that emerge from the vicinity of the object's surface. This lack of deviations would also mean that the remnant of the merger has to have a strongly absorbing surface and must then be a BH for all practical purposes. We conclude that a relationship between the minimal redshift factor and the BH entropy, which was first proposed by 't Hooft, could then be used to set a lower bound on the entropy of the post-merger BH.

gr-qc↗

arXiv2019

A maximal-entropy initial state of the Universe as a microscopic description of inflation

We propose that the initial state of the Universe was an isotropic state of maximal entropy. Such a state can be described in terms of a state of closed, interacting, fundamental strings in their high-temperature Hagedorn phase. The entropy density in this state is equal to the square root of the energy density in Planck units, while the pressure is positive and equal to the energy density. These relations imply a maximally large entropy density and, therefore, a state that cannot be described by a semiclassical spacetime geometry. If one nevertheless insists on an effective semiclassical description of this state, she can do so by ignoring the entropy. This leads to a partially equivalent description in which the pressure appears to be negative and equal in magnitude to the energy density, as if the energy-momentum tensor was that of a cosmological constant. From this effective perspective, the state describes a period of string-scale inflation. The bound state of strings ultimately decays, possibly by a process akin to Hawking radiation, and undergoes a transition into a phase of hot radiation. But, from the effective perspective, the same decay corresponds to the heating of the Universe at the end of inflation. Small quantum mechanical fluctuations in the initial state lead to scale-invariant temperature anisotropies in the hot radiation. The temperature anisotropies are interpreted in the effective description as arising from quantum fluctuations of the curvature and an effective inflaton field. The stringy microscopic description determines the parameters of the model of inflation, as well as the cosmological observables, in terms of the string length scale and coupling strength. Our framework is similar, conceptually, to a recent description of black holes in terms of a maximal entropy state of strings in the Hagedorn phase.

hep-th↗

arXiv2019

Non-singular black holes interiors need physics beyond the standard model

The composition as well as the very existence of the interior of a Schwarzschild black hole (BH) remains at the forefront of open problems in fundamental physics. To address this issue, we turn to Hawking's "principle of ignorance", which says that, for an observer with limited information, all descriptions that are consistent with known physics are equally valid. We compare three different observers who view the BH from the outside and agree on the external Schwarzschild geometry. First, the modernist, who accepts the classical BH as the final state of gravitational collapse, the singularity theorems that underlie this premise and the central singularity that the theorems predict. The modernist is willing to describe matter in terms of quantum fields in curved space but insists on (semi)classical gravity. Second is the skeptic, who wishes to evade any singular behavior by finding a loophole to the singularity theorems within the realm of classical general relativity (GR). The third is a postmodernist who similarly wants to circumvent the singularity theorems but is willing to invoke exotic quantum physics in the gravitational and/or matter sector to do so. The postmodern view suggests that the uncertainty principle can stabilize a classically singular BH in a similar manner to the stabilization of the classically unstable hydrogen atom: Strong quantum effects in the matter and gravitational sectors resolve the would-be singularity over horizon-sized length scales. The postmodern picture then requires a significant departure from (semi)classical gravity, as well as some exotic matter beyond the standard model of particle physics (SM). We find that only the postmodern framework is consistent with what is known so far about BH physics and conclude that a valid description of the BH interior needs matter beyond the SM and gravitational physics beyond (semi)classical GR.

hep-th↗

arXiv2019

Resisting collapse: How matter inside a black hole can withstand gravity

How can a Schwarzschild-sized matter system avoid a fate of gravitational collapse? To address this question, we critically reexamine the arguments that led to the "Buchdahl bound", which implies that the minimal size of a stable, compact object must be larger than nine eighths of its own Schwarzschild radius. Following Mazur and Mottola, and in line with other counterexamples to the singularity theorems, we identify large negative radial pressure extending to the gravitational radius as the essential ingredient for evading the Buchdahl bound. Our results are novel although consistent with many other investigations of models of non-singular black holes. It is shown in particular that a large negative pressure in the framework of classical GR translates into a large positive pressure once quantum physics is incorporated. In this way, a Schwarzschild-sized bound state of closed, interacting fundamental strings in its high-temperature Hagedorn phase can appear to have negative pressure and thus the ability to resist gravitational collapse.

hep-th↗

arXiv2018

Requiem for an ideal clock

The `problem of time' remains an unresolved issue in all known physical descriptions of the Universe. One aspect of this problem is the conspicuous absence of time in the Wheeler-Dewitt equation, which is the analogue of the Schrodinger equation for the Universal wavefunction. Page and Wootters famously addressed this problem by providing a mechanism for effectively introducing time evolution into this timeless cosmological picture. Their method, which is sometimes called the conditional probability interpretation (CPI), requires the identification of an internal clock system that is meant to keep time for the remainder of the Universe. Most investigations into this idea employ the idealized limit of a non-interacting clock system, the so-called ideal clock. However, by allowing for interactions, we have found the counter-intuitive result that a non-interacting clock is not necessarily the optimal choice, even if it is `ideal'. In particular, the uncertainty that is associated with the physical measurement of an atomic clock is found to decrease monotonically as the interactions grow stronger. This observation, which is reinforced by a previous study using a semi-classical clock, paves the way to an independent argument that is based on the energy conservation of any isolated system. Our conclusion is that ideal clocks must be prohibited from the CPI when recovering cosmological time evolution. Interactions are necessary for describing time evolution as a strict matter of principle. Lastly, we also consider the implications of this result for the experience of time in the evolution of the Universe.

quant-ph↗

arXiv2018

The problem with `The Problem of Time'

We investigate three aspects of the supposed problem of time: The disagreement between the treatments of time in general relativity and quantum theory, the problem of recovering time from within an isolated Universe and the prevalence of a unidirectional time flow (i.e., the so-called arrow of time). Under our interpretation, general relativity and quantum theory have complementary time treatments given that they emerge from a theory of a more fundamental nature. To model an isolated Universe, we use the Wheeler-DeWitt equation and then apply the Page-Wootters method of recovering time. It is argued that, if the recovery of an experience of time is indeed viable in this framework, interactions and quantum entanglement are both essential features, even though the former is normally an afterthought or altogether dismissed. As for the one-way arrow of time, this is, from our perspective, a consequence of including the aforementioned interactions. But underlying our interpretation, and pretty much all others, is the necessity for causality. It is this fundamental tenet which accounts for our experience of time but yet can only be postulated. Our conclusion is that the `problem of causality' is what should be the focal point of future investigations.

quant-ph↗