arXiv subjects

Yuki Yokokura

Publications and source records attributed to Yuki Yokokura.

At least 19 recordsLinked to original sources

arXiv2026

Gravitational-wave Echoes Beyond the Hubble Time from Quantum Black Holes

We investigate gravitational-wave echoes in a horizonless compact object model, a non-perturbative solution of the semi-classical Einstein equation that reproduces the entropy-area law from the bulk structure. By employing a model of anisotropic fluids in classical general relativity (GR), we show that odd-parity gravitational waves are not reflected at the object's surface but are trapped inside due to the exponentially strong redshift, and that the echo-delay time extremely exceeds the age of the Universe. Consequently, the echo signals are effectively unobservable, which is consistent with current null results from echo searches. We finally discuss how this quantum black hole and the conventional classical black hole could be distinguished observationally.

gr-qc↗

arXiv2026

Schrödinger Symmetry in Spherically-symmetric Static Mini-superspaces with Matter Fields

Schrödinger symmetry has been shown to emerge in a ``fluid limit" from the full superspace to several mini-superspace models. To investigate one aspect of the robustness of this emergent symmetry, we consider two spherically-symmetric static mini-superspace models with matter fields at the classical level: (i) a Maxwell field with a cosmological constant and (ii) $n$ massless scalar fields. By developing a method based on canonical transformations, we demonstrate that for model (i), 3D Schrödinger symmetry emerges, and the solution is the (anti-)de Sitter Reissner-Nordström spacetime, and for model (ii), $(2+n)$D Schrödinger symmetry appears, and the solution is a generalized Janis-Newman-Winicour spacetime and its ``interior", a Kantowski-Sachs type closed universe. Furthermore, for the vacuum model, we find that 2D Schrödinger symmetry holds with different lapse functions and mini-superspace coordinates, suggesting the potential, yet unconfirmed, covariance of the symmetry. Finally, we propose a physical interpretation of the symmetry under the Hamiltonian constraint $H$: symmetry generators commuting with $H$ map a solution to another one, while those non-commuting with $H$ generate a new theory with the Schrödinger symmetry and the transformed configuration is a solution to the new theory. These results reinforce the robustness of the emergent Schrödinger symmetry and open new frontiers for exploring dynamics of matter and gravity.

gr-qc↗

arXiv2026

Revisiting Spherically Symmetric Spacetime I: Geometro-Hydrodynamics

This series of works revisits the geometry, dynamics, and covariant phase space of spherically symmetric spacetimes with the aim of exploring the thermodynamics of spacetime from their dynamical properties. In this first paper, we examine the geometry from the perspective of a foliation by spherical hypersurfaces. Using the rigging technique, we first define a local frame adapted to these slices and reconstruct the geometry and dynamics fully. We clarify the connection of the frame adapted to constant-radius slices, to the Kodama vector and Misner-Sharp energy. Through frame transformations, we then show that the gravitational dynamics in a general foliation-adapted frame can be interpreted as hydrodynamics, i.e., geometro-hydrodynamics: the Einstein equations exhibit the gravitational analogs of the Euler and Young-Laplace equations, and the spacetime can be viewed as the worldvolume of a concentric stack of "gravitational bubbles" -- spherical collective modes with the Misner-Sharp energy density and a geometric pressure. We apply this framework to apparent horizons and study the dynamics. Finally, we demonstrate that a similar geometro-hydrodynamic picture holds in Lovelock gravity. These results provide a fresh perspective on this class of spacetimes and lay the foundation for understanding their thermodynamic properties.

gr-qc↗

arXiv2025

Effective Dynamics of Spherically Symmetric Static Spacetime

In general relativity, the Einstein equations provide spherically symmetric static spacetimes with dynamics defined as an evolution along the radial coordinate $r$. The geometrical sector becomes a one-dimensional mechanical system, with the Misner-Sharp mass and lapse as canonically conjugate variables, and a vanishing Hamiltonian for pure gravity. Coupling classical or quantum matter fields, or introducing (quantum) corrections to general relativity, then generate a non-vanishing effective Hamiltonian, leading to non-trivial evolutions of the mass and lapse. We illustrate this mechanism through various examples of classical matter fields and identify Hamiltonians describing the effective dynamics of gravity coupled to perfect fluids with linear barotropic equation of state. Finally, we derive effective Hamiltonians that reproduce the gravitational semi-classical dynamics coupled to renormalized quantum matter fields and discuss the conditions for which the singularity at $r=0$ is resolved. In particular, we find a singularity-free black-hole-like solution, stabilized by quantum matter, smoothly transitioning from a bulk with constant negative Ricci scalar to the standard outside Schwarzschild metric. This opens new possibilities for the modeling of both semi-classical corrections and deep quantum effects on the interior structure of self-gravitating compact objects and black holes.

gr-qc↗

arXiv2025

Black Hole from Entropy Maximization

One quantum characterization of a black hole motivated by (local) holography and thermodynamics is that it maximizes thermodynamic entropy for a given surface area. In the context of quantum gravity, this could be more fundamental than the classical characterization by a horizon. As a step, we explore this possibility by solving the 4D semi-classical Einstein equation with many matter fields. For highly-excited spherically-symmetric static configurations, we apply local typicality and estimate the entropy including self-gravity to derive its upper bound. The saturation condition uniquely determines the entropy-maximized configuration: self-gravitating quanta condensate into a radially-uniform dense configuration with no horizon, where the self-gravity and a large quantum pressure induced by the curvatures are balanced and no singularity appears. The interior metric is a self-consistent and non-perturbative solution in Planck's constant. The maximum entropy, given by the volume integral of the entropy density, agrees with the Bekenstein-Hawking formula through self-gravity, deriving the Bousso bound for thermodynamic entropy. Finally, 10 future prospects are discussed, leading to a speculative view that the configuration represents a quantum-gravitational condensate in a semi-classical manner.

hep-th↗

arXiv2024

Imaging a semi-classical horizonless compact object with strong redshift

The recent advancements in black hole imaging have opened a new era of probing horizon-scale physics with electromagnetic radiation. However, a feature of the observed images, a bright ring encircling a relatively dark region, has not sufficiently proved the existence of event horizons. It thus requires extreme care when studying the possibility of using such image features to examine quantum effects that may change the classical picture of black holes slightly or drastically. In this work, we investigate the image of a horizonless compact object, whose interior metric satisfies the 4D semi-classical Einstein equation non-perturbatively for the Planck constant, and whose entropy agrees with the Bekenstein-Hawking formula. Although the absence of an event horizon allows light rays to pass through the dense interior, the extremely strong redshift significantly darkens the image, making it almost identical to the classical black-hole image. In particular, if there is light emission a bit inside the surface of the object, the intensity around the inner shadow is slightly enhanced, which could be a future observable prediction to characterize the object. We also find through a phenomenological parameter that the image is further darkened due to interactions inside. Thus, the image is consistent with current observations, and the object could be a candidate for black holes in quantum theory.

gr-qc↗

arXiv2024

4D Weyl Anomaly and Diversity of the Interior Structure of Quantum Black Hole

We study the interior metric of 4D spherically symmetric static black holes by using the semi-classical Einstein equation and find a consistent class of geometries with large curvatures. We approximate the matter fields by conformal fields and consider the contribution of the 4D Weyl anomaly, giving a state-independent constraint. Combining this with an equation of state yields an equation that determines the interior geometry completely. We explore the solution space of the equation in a non-perturbative manner for $\hbar$. First, we find four types of asymptotic behaviors and examine the general features of the solutions. Then, by imposing physical conditions, we obtain approximately a general class of interior geometries: various combinations of dilute and dense structures without a horizon or singularity. This represents the diversity of the interior structure. Finally, we show that the number of possible patterns of such interior geometries corresponds to the Bekenstein-Hawking entropy.

hep-th↗

arXiv2024

Self-Gravity and Bekenstein-Hawking Entropy

We study the effect of self-gravity on entropy by directly solving the 4D semi-classical Einstein equation. In particular, we focus on whether the Bekenstein-Hawking formula holds when self-gravity is extremely strong. As an example, we consider a simple spherically symmetric static configuration consisting of many quanta and construct a self-consistent non-perturbative solution for $\hbar$ in which the entropy exactly follows the area law for many local degrees of freedom of any kind. This can be a candidate for black holes in quantum theory. It represents a compact dense configuration with near-Planckian curvatures, and the interior typically behaves like a local thermal state due to particle creation. Here, the information content is stored in the interior bulk, and the self-gravity plays an essential role in changing the entropy from the volume law to the area law. We finally discuss implications to black holes in quantum gravity and a speculative view of entropy as a gravitational charge.

hep-th↗

arXiv2022

Interior Metric of Slowly Formed Black Holes in a Heat Bath

We study a spherical black hole formed slowly in a heat bath in the context of ordinary field theory, which we expect to have the typical properties of black holes. We assume that the matter field is conformal and that the metric satisfies the semi-classical Einstein equation $G_{μν}=8πG \langle ψ| T_{μν}|ψ\rangle$, where $|ψ\rangle$ is the wave function of the matter field. Then as a necessary condition, its trace part must be satisfied, $G^μ_μ=8πG \langle ψ| T^μ_μ|ψ\rangle$, whose right-hand side is independent of $|ψ\rangle$ and is determined only by the metric through the 4-dimensional Weyl anomaly. With some physically reasonable assumptions, this equation restricts the interior metric to a certain class. Such metrics are approximately warped products of $AdS_2$ and $S^2$ with almost Planckian curvature. Among them, we find one that is consistent with Hawking radiation and is smoothly connected to the exterior Schwarzschild metric slightly outside the Schwarzschild radius. This leads to a picture that the black hole is a dense object with a surface (not a horizon), which evaporates due to Hawking-like radiation when taken out of the bath. Other solutions represent objects that are larger in size than a black hole, which may be useful for analyzing ultra-dense stars.

hep-th↗

arXiv2021

Planckian Physics Comes Into Play At Planckian Distance From Horizon

In the background of a gravitational collapse, we compute the transition amplitudes for the creation of particles for distant observers due to higher-derivative interactions in addition to Hawking radiation. The amplitudes grow exponentially with time and become of order 1 when the collapsing matter is about a Planck length outside the horizon. As a result, the effective theory breaks down at the scrambling time, invalidating its prediction of Hawking radiation. Planckian physics comes into play to decide the fate of black-hole evaporation.

hep-th↗

arXiv2021

Distance between collapsing matter and trapping horizon in evaporating black holes

Assuming that the vacuum energy-momentum tensor is not exceptionally large, we consider 4D evaporating black holes with spherical symmetry and evaluate the proper distance $ΔL$ between the time-like apparent horizon and the surface of the collapsing matter after it has entered the apparent horizon. We show that $ΔL$ can never be larger than $\mathcal{O}(n^{3/2}\ell_p)$ when the black hole is evaporated to $1/n$ of its initial mass, as long as $n \ll a^{2/3}/\ell_p^{2/3}$ (where $a$ is the Schwarzschild radius and $\ell_p$ is the Planck length). For example, the distance between the matter and the apparent horizon must be Planckian at the Page time.

gr-qc↗

arXiv2020

Firewall From Effective Field Theory

For an effective field theory in the background of an evaporating black hole with spherical symmetry, we consider non-renormalizable interactions and their relevance to physical effects. The background geometry is determined by the semi-classical Einstein equation for an uneventful horizon where the vacuum energy-momentum tensor is small for freely falling observers. Surprisingly, after Hawking radiation appears, the transition amplitude from the Unruh vacuum to certain multi-particle states grows exponentially with time for a class of higher-derivative operators after the collapsing matter enters the near-horizon region, despite the absence of large curvature invariants. Within the scrambling time, the uneventful horizon transitions towards a firewall, and eventually the effective field theory breaks down.

hep-th↗

arXiv2020

Black Hole as a Quantum Field Configuration

We describe 4D evaporating black holes as quantum field configurations by solving the semi-classical Einstein equation $G_{μν}=8πG \langle ψ|T_{μν}|ψ\rangle$ and quantum matter fields in a self-consistent manner. As the matter fields we consider $N$ massless free scalar fields ($N$ is large). We find a spherically symmetric self-consistent solution of the metric $g_{μν}$ and state $|ψ\rangle$. Here, $g_{μν}$ is locally $AdS_2\times S^2$ geometry, and $|ψ\rangle$ provides $\langle ψ|T_{μν}|ψ\rangle=\langle0|T_{μν}|0 \rangle+T_{μν}^{(ψ)}$, where $|0\rangle$ is the ground state of the matter fields in the metric and $T_{μν}^{(ψ)}$ consists of the excitation of s-waves that describe the collapsing matter and Hawking radiation with the ingoing negative energy flow. This object is supported by a large tangential pressure $\langle0|T^θ_θ|0 \rangle$ due to the vacuum fluctuation of the bound modes with large angular momenta. This describes the interior of the black hole when the back reaction of the evaporation is considered. The black hole is a compact object with a surface (instead of horizon) that looks like a conventional black hole from the outside and eventually evaporates without a singularity. If we count the number of self-consistent configurations $\{|ψ\rangle\}$, we reproduce the area law of the entropy. This tells that the information is carried by the s-waves inside the black hole. $|ψ\rangle$ also describes the process that the negative ingoing energy flow created with Hawking radiation is superposed on the collapsing matter to decrease the total energy while the total energy density remains positive. As a special case, we consider conformal matter fields and show that the interior metric is determined by the matter content of the theory, which leads to a new constraint to the matter content.

hep-th↗

arXiv2020

An Analytic Description of Semi-Classical Black-Hole Geometry

We study analytically the spacetime geometry of the black-hole formation and evaporation. As a simplest model of the collapse, we consider a spherical thin shell, and take the back-reaction from the negative energy of the quantum vacuum state. For definiteness, we will focus on quantum effects of s-waves. We obtain an analytic solution of the semi-classical Einstein equation for this model, that provides an overall description of the black hole geometry form the formation to evaporation. As an application of this result, we find its interesting implication that, after the collapsing shell enters the apparent horizon, the proper distance between the shell and the horizon remains as small as the Planck length even when the difference in their areal radii is of the same order as the Schwarzschild radius. The position of the shell would be regarded as the same place to the apparent horizon in the semi-classical regime of gravity.

hep-th↗

arXiv2018

Thermal pure state path integral and emergent symmetry

We investigate a thermally isolated quantum many-body system with an external control represented by a time-dependent parameter. We formulate a path integral in terms of thermal pure states and derive an effective action for trajectories in a thermodynamic state space, where the entropy appears with its conjugate variable. In particular, for quasi-static operations, the symmetry for the uniform translation of the conjugate variable emerges in the path integral. This leads to the entropy as a Noether invariant.

cond-mat.stat-mech↗

arXiv2018

Thermodynamical path integral and emergent symmetry

We investigate a thermally isolated quantum many-body system with an external control represented by a step protocol of a parameter. The propagator at each step of the parameter change is described by thermodynamic quantities under some assumptions. For the time evolution of such systems, we formulate a path integral over the trajectories in the thermodynamic state space. In particular, for quasi-static operations, we derive an effective action of the thermodynamic entropy and its canonically conjugate variable. Then, the symmetry for the uniform translation of the conjugate variable emerges in the path integral. This leads to the entropy as a Noether invariant in quantum mechanics.

cond-mat.stat-mech↗

arXiv2018

Back Reaction of 4D Conformal Fields on Static Geometry

Static, spherically symmetric solutions to the semi-classical Einstein equation are studied, including the effect of the quantum energy-momentum tensor for conformal matters with 4D Weyl anomaly. Through both perturbative and non-perturbative methods, we show that the quantum effect can play a crucial role in shaping the near-horizon geometry, and that the existence of the horizon requires fine-tuning.

hep-th↗

arXiv2017

A Model of Black Hole Evaporation and 4D Weyl Anomaly

We analyze time evolution of a spherically-symmetric collapsing matter from a point of view that black holes evaporate by nature. We consider conformal matters and solve the semi-classical Einstein equation $G_{μν}=8πG \langle T_{μν} \rangle$ by using the 4-dimensional Weyl anomaly with a large $c$ coefficient. Here $\langle T_{μν} \rangle$ contains the contribution from both the collapsing matter and Hawking radiation. The solution indicates that the collapsing matter forms a dense object and evaporates without horizon or singularity, and it has a surface but looks like an ordinary black hole from the outside. Any object we recognize as a black hole should be such an object.

hep-th↗