arXiv subjects

Gabor Kunstatter

Publications and source records attributed to Gabor Kunstatter.

At least 19 recordsLinked to original sources

arXiv2026

Scalar Field Model for Dark Matter Spikes Surrounding Sgr A$^$ and M87$^$

Theoretical models suggest that the adiabatic growth of a black hole immersed in dark matter can lead to the formation of high density regions of dark matter, known as ``spikes'', near the black hole event horizon. The density of these spikes is determined theoretically and observationally to be a power law of the form $\rho(r) \propto r^{-\gamma_\text{sp}}$. It has been shown that the spike can potentially have a detectable impact on the emitted gravitational waves and shadow radius of the central black hole. In this work, we model the dark matter spike using a real scalar field with a non-standard potential. More specifically we ``reverse engineer'' the equations of motion to find a potential for the scalar field that permits a solution to the equations of motion with desired energy density and reasonable background geometry. We show that the emerging geometry is testable. In addition, the fact that the solution is derived from a covariant action makes it possible to study gravitational perturbations of the black hole in the presence of a spike including the backreaction of the spike.

gr-qc↗

arXiv2026

${\cal N}=4$ supersymmetric Yang-Mills thermodynamics to order $\lambda^{5/2}$

We calculate the resummed perturbative free energy of ${\cal N} = 4$ supersymmetric Yang-Mills in four spacetime dimensions (SYM$_{44}$) to order $\lambda^{5/2}$ in the 't Hooft coupling at finite temperature and zero chemical potential. All infrared divergences cancel when we include contributions from SYM$_{44}$ ring diagrams and the final result is both ultraviolet and infrared finite. Our result has special significance since order $\lambda^{5/2}$ is the highest order calculation that can be done with perturbation theory, because there are nonperturbative effects associated with the magnetic mass scale that come into play at order $\lambda^3$. We compare results obtained with regularization by dimensional reduction (RDR), which preserves supersymmetry, and canonical dimensional regularization (DR). We also compare with a generalized Pad\'e approximant constructed by matching the weak coupling result at order $\lambda^2$ and the large $N_c$ strong coupling result at order $\lambda^{-3/2}$. Finally we make a comparison between our result and the QCD free energy and show that SYM$_{44}$ has better convergence properties.

hep-th↗

arXiv2025

Quantum-Corrected Bondi Mass for 2D Hawking Radiation

We derive the Hamiltonian for general semi-classical 2D dilaton gravity, beginning with the complete action including the Polyakov action and Gibbons-Hawking-York boundary term. The value of the Hamiltonian yields a generalized Brown-York quasi-local mass function, and the ADM and Bondi masses are obtained in the appropriate limits. The Bondi mass is equal to the classical mass plus a correction term given by the transformation between initial and final inertial frames. We test the expression for the Bondi mass in the RST model, which can be treated analytically, and in several other models numerically. We find it is monotonically decreasing and remains positive throughout the evaporation process for asymptotically flat black holes.

gr-qc↗

arXiv2025

Evaporation of regular black holes in 2D dilaton gravity

We present a general class of non-singular black holes in semi-classical, two-dimensional dilaton gravity, with a focus on a Bardeen-like model. The equations of motion for an evaporating black hole including backreaction are solved numerically. The apparent horizons evaporate smoothly in finite time to form a compact trapped region. Backreaction effects lead to the formation of additional trapped and anti-trapped regions after the primary black hole becomes un-trapped. Numerical simulations of microscopic black holes yield a final spacetime that is free of apparent horizons and Cauchy horizons. This would imply that the evaporation of regular black holes is a unitary process.

gr-qc↗

arXiv2024

Spontaneous Symmetry Breaking To GR in SO(4,2) Gravitational Yang-Mills Theory

We consider a Yang-Mills type gauge theory of gravity based on the conformal group SO(4,2) coupled to a conformally invariant real scalar field. The goal is to generate fundamental dimensional constants via spontaneous breakdown of the conformal symmetry. In the absence of other matter couplings the resulting theory resembles Weyl-Einstein gravity, {with the Newton constant given by the square of the (constant) vacuum expectation value of the scalar, the cosmological constant determined by the quartic coupling constant of the scalar field and the Weyl to Einstein transition scale determined by the Yang-Mills coupling constant.} The emergent theory in the long-wave-length limit is Einstein gravity with cosmological constant. As an illustrative example we present an exact spherically symmetric cosmological solution with perfect fluid energy-momentum tensor that reduces to $\Lambda$FRW in the long-wavelength limit.

gr-qc↗

arXiv2024

No Drama in 2D Black Hole Evaporation

We numerically calculate the spacetime describing the formation and evaporation of a regular black hole in 2D dilaton gravity. The apparent horizons evaporate smoothly in finite time to form a compact trapped region. We nevertheless see rich dynamics; an anti-trapped region forms alongside the black hole, and additional compact trapped and anti-trapped regions are formed by backreaction effects as the mass radiates away. The spacetime is asymptotically flat at future null infinity and is free of singularities and Cauchy horizons. These results suggest that the evaporation of regular 2D black holes is unitary.

gr-qc↗

arXiv2024

The effect of anisotropy on the formation of heavy quarkonium bound states

We study the real part of the static potential of a heavy quark-antiquark system in an anisotropic plasma medium. We use a quasi-particle approach where the collective dynamics of the plasma constituents is described using hard-loop perturbation theory. The parton distribution function is characterized by a set of parameters that can accurately describe the anisotropy of the plasma produced in a heavy ion collision. We calculate the potential numerically in strongly anisotropic systems and study the angular dependence of the distortion of the potential relative to the isotropic one. We obtain an analytic expression for the real part of the heavy quark potential in the limit of weak anisotropy using a model that expresses the potential in terms of effective screening masses that depend on the anisotropy parameters and the orientation of the quark-antiquark pair. A 1-dimensional potential is formulated in terms of angle averaged screening masses that incorporate the anisotropy of the medium into a radial coordinate. We solve the corresponding Schrödinger equation and show that the magnitude of the binding energy typically increases with anisotropy. Anisotropy can play an important role, especially in states with non-zero angular momentum. This means that the number of bound states that are formed could depend on specific characteristics of the anisotropy of the plasma. Our study suggests that plasma anisotropy plays an important role in the dynamics of heavy quarkonium and motivates further study.

hep-ph↗

arXiv2024

Evidence for universal flow and characteristics of early time thermalization in a scalar field model for heavy ion collisions

We study numerically the evolution of an expanding strongly self-coupled real scalar field. We use a conformally invariant action that gives a traceless energy-momentum tensor and is better suited to model the early time behaviour of a system such as QCD, whose action is also conformally invariant.We consider asymmetric initial conditions and observe that when the system is initialized with non-zero spatial eccentricity, the eccentricity decreases and the elliptic flow coefficient increases. We look at a measure of transverse pressure asymmetry that has been shown to behave similarly to the elliptic flow coefficient in hydrodynamic systems and show that in our system their behaviour is strikingly similar. We show that the derivative of the transverse velocity is proportional to the gradient of the energy in Milne coordinates and argue that this result means that transverse velocity initially develops in the same way that it does in hydrodynamic systems. We conclude that some aspects of the early onset of hydrodynamic behaviour that has been observed in quark-gluon plasmas are seen in our numerical simulation of strongly coupled scalar fields.

hep-th↗

arXiv2024

Spacetime metrics and ringdown waveforms for galactic black holes surrounded by a dark matter spike

Theoretical models suggest the existence of a dark matter spike surrounding the supermassive black holes at the core of galaxies. The spike density is thought to obey a power law that starts at a few times the black hole horizon radius and extends to a distance, $R_\text{sp}$, of the order of a kiloparsec. We use the Tolman-Oppenheimer-Volkoff equations to construct the spacetime metric representing a black hole surrounded by such a dark matter spike. We consider the dark matter to be a perfect fluid, but make no other assumption about its nature. The assumed power law density provides in principle three parameters with which to work: the power law exponent $γ_\text{sp}$, the external radius $R_\text{sp}$, and the spike density $ρ_\text{DM}^\text{sp}$ at $R_\text{sp}$. These in turn determine the total mass of the spike. We focus on Sagittarius A* and M87 for which some theoretical and observational bounds exist on the spike parameters. Using these bounds in conjunction with the metric obtained from the Tolman-Oppenheimer-Volkoff equations, we investigate the possibility of detecting the dark matter spikes surrounding these black holes via the gravitational waves emitted at the ringdown phase of black hole perturbations. Our results suggest that if the spike to black hole mass ratio is roughly constant, greater mass black holes require relatively smaller spike densities to yield potentially observable signals. We find that is unlikely for the spike in M87 to be detected via the ringdown waveform with currently available techniques unless its mass is roughly an order of magnitude larger than existing observational estimates. However, given that the signal increases with black hole mass, spikes might be observable for more massive galactic black holes in the not too distant future.

astro-ph.GA↗

arXiv2023

Effect of dark matter on galactic black hole ringdown waveforms and shadows

We calculate the effect of dark matter on the ringdown waveform and shadow of supermassive black holes at the core of galaxies. Our main focus is on the supermassive black hole at the core of M87, which is large enough to allow for viable observational data. We compare the effects of a dark matter spike to those expected from a galactic halo of the same mass. Our calculation for the halo starts from the Hernquist density function and assumes anisotropic pressure that is zero in the radial direction. The resulting Tolman-Oppenheimer-Volkoff equations allow the corresponding metric to be obtained analytically in closed form. The geometry of the anisotropic dark matter spike is the same as that obtained in [{\it ApJ} {\bf 940} 33 (2022)] under the assumption of isotropy. The effect of the spike is orders of magnitude more significant than the halo as long as the distribution scale of the latter is within a few orders of magnitude of the value expected from observations. Our results indicate that the impact of the spike surrounding M87* on the ringdown waveform may in principle be detectable. Finally, we point out the somewhat surprising fact that existing Event Horizon Telescope observations of black hole shadows are within an order of magnitude from being able to detect, or rule out, the presence of a spike.

gr-qc↗

arXiv2022

Isotropization of a rotating and longitudinally expanding $ϕ^4$ scalar system

We present numerical simulations for the evolution of an expanding system of massless scalar fields with quartic coupling. By setting a rotating, non-isotropic initial configuration, we compute the energy density, the transverse and longitudinal pressures and the angular momentum of the system. We compare the time scales associated with the isotropization and the decay of the initial angular momentum due to the expansion, and show that even for fairly large initial angular momentum, it decays significantly faster than the pressure anisotropy.

hep-th↗

arXiv2021

Scalar Perturbations and Stability of a Loop Quantum Corrected Kruskal Black Hole

We investigate the massless scalar field perturbations of a new loop quantum gravity motivated regular black hole proposed by Ashtekar {\it et al.} in [Phys.Rev.Lett. 121, 241301 (2018), Phys.Rev.D 98, 126003 (2018)]. The spacetime of this black hole is distinguished by its asymptotic properties: in Schwarzschild coordinates one of the metric functions diverges as $r\to \infty$ even though the spacetime is asymptotically flat. We show that despite this unusual asymptotic behavior, the quasinormal mode potential is well defined everywhere when Schwarzschild coordinates are used. We propose a useful approximate form of the metric, which allows us to produce quasinormal mode frequencies and ringdown waveforms to high accuracy with manageable computation times. Our results indicate that this black hole model is stable against massless scalar field perturbations. We show that, compared to the Schwarzschild black hole, this black hole oscillates with higher frequency and less damping. We also observe a qualitative difference in the power-law tail of the ringdown waveform between this black hole model and the Schwarzschild black hole. This suggests the quantum corrections affect the behavior of the waves at large distances from the black hole.

gr-qc↗

arXiv2020

Scalar Perturbations of a Single-Horizon Regular Black Hole

We investigate the massless scalar field perturbations, including the quasinormal mode spectrum and the ringdown waveform, of a regular black hole spacetime that was derived via the Loop Quantum Gravity inspired polymer quantization of spherical $4$D black holes. In contrast to most, if not all, of the other regular black holes considered in the literature, the resulting nonsingular spacetime has a single bifurcative horizon and hence no mass inflation. In the interior, the areal radius decreases to a minimum given by the Polymerization constant, $k$, and then re-expands into a Kantowski-Sachs universe. We find indications that this black hole model is stable against small scalar perturbations. We also show that an increase in the magnitude of $k$ will decrease the height of the QNM potential and gives oscillations with lower frequency and less damping.

gr-qc↗

arXiv2020

Escape from the Quantum Pigeon Conundrum

It has recently been argued in Aharonov et. al. (2016) that quantum mechanics violates the Pigeon Counting Principle (PCP) which states that if one distributes three pigeons among two boxes there must be at least two pigeons in one of the boxes. However, this conclusion cannot justified by rigorous theoretical arguments. The issue is further complicated by experimental confirmation of the transition amplitudes predicted in this paper that nevertheless do not support the conclusion of PCP violation. Here we prove via a set of operator identities that the PCP is not violated within quantum mechanics, regardless of interpretation.

quant-ph↗

arXiv2019

A Non-Equilibrium Approach To Holographic Superconductors Using Gradient Flow

We study a charged scalar field in a bulk 3+1 dimensional anti-deSitter spacetime with a planar black hole background metric. Through the AdS/CFT correspondence this is equivalent to a strongly coupled field theory in 2+1 dimensions describing a superconductor. We use the gradient flow method and solve the flow equations numerically between two fixed points: a vacuum solution and a hairy black hole solution. We study the corresponding flow on the boundary between a normal metal phase and a superconducting phase. We show how the gradient flow moves fields between two fixed points in a way that minimizes the free energy of the system. At the fixed points of the flow the AdS/CFT correspondence provides an equivalence between the Euclidean on-shell action in the bulk and the free energy of the boundary, but it does not tell us about fields away from equilibrium. However, we can formally link static off-shell configurations in the bulk and in the boundary at the same point along the flow. For quasi-static evolution at least, it may be reasonable to think of this link as an extension of the AdS/CFT correspondance.

hep-th↗

arXiv2018

Quantum Mechanics of the Interior of the Russo-Susskind-Thorlacius Black Hole

We study the quantum mechanics of homogeneous black hole interiors in the RST model of 2D gravity. The model, which contains a dilaton and metric, includes radiation back-reaction terms and is exactly solvable classically. The reduced phase space is four dimensional. The equations for one pair of variables can be trivially solved. The dynamics of the remaining degree of freedom, namely the dilaton, is more interesting and corresponds to that of a particle on the half line in a linear potential with time dependent coupling. We construct the self-adjoint extension of the corresponding quantized Hamiltonian and numerically solve the time dependent Schr$\ddot{\mbox{o}}$dinger equation for Gaussian initial data. As expected the singularity is resolved and the expectation value of the dilaton oscillates between a minimum and maximum, which both gradually decrease with time due to the time dependence in the potential. In the classical black hole spacetime, the maximum value of the dilaton corresponds to the size of the horizon while the minimum is the singularity. The quantum dynamics, therefore, corresponds at the semi-classical level to an evaporating black hole. The rate of quantum fluctuations increases as the system evolves but intriguingly, at longer times the expectation value of the radius undergoes "revivals" in which the amplitude of oscillations between minimum and maximum temporarily increases. These revivals are also characteristic of the quantum dynamics of the {\it time independent} quantum linear potential.

gr-qc↗

arXiv2018

Smooth and sharp creation of a spherical shell for a $(3+1)$-dimensional quantum field

We study the creation of a spherical, finite radius source for a quantized massless scalar field in 3+1 dimensions. The goal is to model the breakdown of correlations that has been proposed to occur at the horizon of an evaporating black hole. We do this by introducing at fixed radius $r=a$ a one parameter family of self-adjoint extensions of the three dimensional Laplacian operator that interpolate between the condition that the values and the derivatives on the two sides of $r=a$ coincide for $t\le0$ (no wall) and the two-sided Dirichlet boundary condition for $t \ge 1/λ$ (fully-developed wall). Creation of the shell produces null, spherical pulses of energy on either side of the shell, one ingoing and the other outgoing. The renormalized energy density $\langle T_{00}\rangle$ diverges to positive infinity in the outgoing energy pulse, just outside the light cone of the fully-formed wall at $t=1/λ$. Unlike in the 3+1 point source creation, there is no persistent memory cloud of energy. As in the creation of a 1+1 dimensional wall, the response of an Unruh-DeWitt detector in the post-shell region is independent of the time scale for shell formation and is finite. The latter property casts doubt on the efficacy of this mechanism for firewall creation.

gr-qc↗

arXiv2017

Exact time-dependent states for throat quantized toroidal AdS black holes

We investigate exact non-stationary quantum states of vacuum toroidal black holes with a negative cosmological constant in arbitrary dimensions using the framework of throat quantization pioneered by Louko and Mäkelä for Schwarzschild black holes. The system is equivalent to a harmonic oscillator on the half line, in which the central singularity is resolved quantum mechanically by imposing suitable boundary conditions that preserve unitarity. We identify two suitable families of exact time-dependent wave functions with Dirichlet or Neumann boundary conditions at the location of the classical singularity. We find that for highly non-stationary states of large-mass black holes, quantum fluctuations are not negligible in one family, while they are greatly suppressed in the other. The latter, therefore, may provide candidates for describing the dynamics of semi-classical black holes.

gr-qc↗