arXiv subjects

Harvey S. Reall

Publications and source records attributed to Harvey S. Reall.

At least 19 recordsLinked to original sources

arXiv2026

The BTZ black hole, the Third Law and gravitational collapse

We prove that a Third Law of black hole mechanics holds for the BTZ black hole in 3d gravity coupled to matter obeying the dominant energy condition. This law states that initial data containing a trapped surface cannot evolve in finite time to a black hole that coincides with extremal BTZ on the event horizon, for any choice of boundary conditions at infinity. The result is proved by defining a quasilocal energy and angular momentum and using spinorial methods to establish a BPS inequality that is saturated by the extremal BTZ solution. Nevertheless, we show that gravitational collapse of a massless scalar field can result in the formation of an extremal BTZ black hole in finite time. The difference between these results arises because gravitational collapse occurs in the Neveu-Schwarz sector, whereas extremal BTZ is supersymmetric in the Ramond sector. Solutions that settle down to extremal BTZ in infinite time along the event horizon are also discussed.

gr-qc↗

arXiv2026

Formation of extremal Reissner-Nordström black holes: insights from numerics

An extremal Reissner-Nordström black hole can form in finite time in the gravitational collapse of a massless charged scalar field. The proof of this is based on the method of characteristic gluing, which involves making an Ansatz for the scalar field at the horizon. We perform a numerical investigation of the characteristic gluing procedure for several different Ansätze. In each case, gluing is possible only if the final black hole mass is large enough. We find that the minimum required mass varies significantly for different Ansätze. We also consider the effect of including a mass term for the scalar field. In this case, for each Ansatz we determine the maximum mass-to-charge ratio for the scalar field such that gluing is possible. Analogous results are obtained for a non-zero cosmological constant.

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arXiv2026

Violation of the third law of black hole mechanics in vacuum gravity

We demonstrate numerically the existence of solutions of five-dimensional vacuum gravity describing the formation, in finite time, of an extremal rotating black hole from a pre-existing Schwarzschild black hole. This is the first example of a violation of the third law of black hole mechanics in vacuum gravity and demonstrates that the third law is false independently of any matter model. We also demonstrate the existence of solutions describing the formation, in finite time, of an extremal rotating black hole from vacuum initial data that does not contain a black hole.

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arXiv2026

The initial data of effective field theories of relativistic viscous fluids and gravity

There has been recent progress in developing well-posed theories of relativistic viscous hydrodynamics and of gravitational effective field theories. These have in common the feature that they introduce unphysical degrees of freedom. We address the problem of how these should be treated. We propose a ''reduction of order'' approach which is applied not at the level of equations of motion but only to initial data. This specifies uniquely the data for the unphysical modes in terms of the data for the physical modes. We argue that the apparent breaking of Lorentz invariance associated with this approach is not a problem provided one restricts to Lorentz frames for which the assumptions of effective field theory are manifestly valid.

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arXiv2025

On the third law of black hole mechanics for supersymmetric black holes

Recently it has been shown that the third law of black hole mechanics can be violated: an exactly extremal Reissner-Nordstrom black hole can form in finite time in gravitational collapse of matter with a large charge to mass ratio. However, it has also been proved that this cannot happen if the matter satisfies a ``supersymmetric'' lower bound on its energy in terms of its charge. This paper proves an analogous result for black holes with a negative cosmological constant. The result states that a supersymmetric Kerr-Newman-anti de Sitter black hole cannot form in gravitational collapse of charged matter satisfying the supersymmetric bound. The results for zero or negative cosmological constant are extended to apply to two-sided black holes: it is proved that an initially non-extremal black hole cannot evolve to a supersymmetric black hole in finite time, irrespective of whether or not the initial black hole was formed in gravitational collapse.

gr-qc↗

arXiv2025

Ill-posedness of the Cauchy problem for linearized gravity in a cavity with conformal boundary conditions

We consider Lorentzian General Relativity in a cavity with a timelike boundary, with conformal boundary conditions and also a generalization of these boundary conditions. We focus on the linearized gravitational dynamics about the static empty cavity whose boundary has spherical spatial geometry. It has been recently shown that there exist dynamical instabilities, whose angular dependence is given in terms of spherical harmonics $Y_{\ell m}$, and whose coefficient of exponential growth in time goes as $\sim \ell^{1/3}$. We use these modes to construct a sequence of solutions for which the initial data converge to zero as $\ell \rightarrow \infty$ but for which the solution itself does not converge to zero. This implies a lack of continuity of solutions on initial data, which shows that the initial value problem with these boundary conditions is not well-posed. This is in tension with recent mathematical work on well-posedness for such boundary conditions.

gr-qc↗

arXiv2025

A third law of black hole mechanics for supersymmetric black holes and a quasi-local mass-charge inequality

It has recently been proved that a third law of black hole mechanics does not hold for Einstein-Maxwell theory coupled to a massless charged scalar field: there exist solutions that describe gravitational collapse to form an exactly extremal Reissner-Nordström black hole in finite time. In this paper it is proved that such solutions do not exist in theories with matter fields satisfying a local mass-charge inequality. In such a theory, if a 2-surface has the same metric, extrinsic curvature, and Maxwell field as a cross-section of an extremal Reissner-Nordström horizon then this surface cannot have a compact interior and so cannot be a horizon cross-section of a black hole formed in gravitational collapse. This result is proved using spinorial techniques, which are also used to prove a mass-charge inequality for a modified version of the Dougan-Mason quasi-local mass.

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arXiv2024

Evolution of creases on the event horizon of a black hole merger

A generic black hole merger occurs through a restructuring of creases (sharp edges) on the event horizon. This process is studied for a black hole merger in the limit of infinite mass ratio, for which constructing the event horizon reduces to finding a null hypersurface that asymptotes to a Rindler horizon in the Kerr spacetime. Geometrical properties of the creases on this horizon are determined and the results are compared with the predictions of an exact local description of the event horizon in a generic merger. The crease set is shown to have finite area. A recently proposed expression for the gravitational entropy of a crease is shown to diverge at the instant of merger. Caustics on (and off) the event horizon are determined by exploiting the correspondence with the problem of gravitational lensing by a Kerr black hole. Caustics form an "astroid tube" in spacetime, two edges of which lie on the event horizon of the merger. Perturbative expressions for the location of this tube are presented, extending previous work to much higher perturbative order.

gr-qc↗

arXiv2024

A non-perturbative second law of black hole mechanics in effective field theory

We describe a method for defining dynamical black hole entropy in gravitational effective field theories (EFTs). The entropy is constructed order by order in derivatives. For any fixed number of derivatives, the entropy satisfies a non-perturbative second law of black hole mechanics if the black hole remains within the regime of validity of EFT. In equilibrium the entropy reduces to the Wald entropy. It reduces to the entropy defined by Hollands et al in theories of vacuum gravity with up to 10 derivatives.

hep-th↗

arXiv2023

Creases, corners and caustics: properties of non-smooth structures on black hole horizons

The event horizon of a dynamical black hole is generically a non-smooth hypersurface. We classify the types of non-smooth structure that can arise on a horizon that is smooth at late time. The classification includes creases, corners and caustic points. We prove that creases and corners form spacelike submanifolds of dimension $2,1$ and that caustic points form a set of dimension at most $1$. We classify "perestroikas" of these structures, in which they undergo a qualitative change at an instant of time. A crease perestroika gives an exact local description of the event horizon near the "instant of merger" of a generic black hole merger. Other crease perestroikas describe horizon nucleation or collapse of a hole in a toroidal horizon. Caustic perestroikas, in which a pair of caustic points either nucleate or annihilate, provide a mechanism for creases to decay. We argue that properties of quantum entanglement entropy suggest that creases might contribute to black hole entropy. We explain that a "Gauss-Bonnet" term in the entropy is non-topological on a non-smooth horizon, which invalidates previous arguments against such a term.

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arXiv2022

Dynamical Black Hole Entropy in Effective Field Theory

In recent work, Hollands, Kovács and Reall have built on previous work of Wall to provide a definition of dynamical black hole entropy for gravitational effective field theories (EFTs). This entropy satisfies a second law of black hole mechanics to quadratic order in perturbations around a stationary black hole. We determine the explicit form of this entropy for the EFT of 4d vacuum gravity including terms in the action with up to 6 derivatives. An open question concerns the gauge invariance of this definition of black hole entropy. We show that gauge invariance holds for the EFT of vacuum gravity with up to 6 derivatives but demonstrate that it can fail when 8 derivative terms are included. We determine an entropy for Einstein-Gauss-Bonnet theory by treating it as an EFT with vanishing 6 derivative terms.

hep-th↗

arXiv2022

A stationary black hole must be axisymmetric in effective field theory

The black hole rigidity theorem asserts that a rotating stationary black hole must be axisymmetric. This theorem holds for General Relativity with suitable matter fields, in four or more dimensions. We show that the theorem can be extended to any diffeomorphism invariant theory of vacuum gravity, assuming that this is interpreted in the sense of effective field theory, with coupling constants determined in terms of a ``UV scale'', and that the black hole solution can locally be expanded as a power series in this scale.

gr-qc↗

arXiv2022

The second law of black hole mechanics in effective field theory

We investigate the second law of black hole mechanics in gravitational theories with higher derivative terms in the action. Wall has described a method for defining an entropy that satisfies the second law to linear order in perturbations around a stationary black hole. We show that this can be extended to define an entropy that satisfies the second law to quadratic order in perturbations, provided that one treats the higher derivative terms in the sense of effective field theory. We also address some outstanding issues with Wall's method, in particular, its gauge invariance and its relation to the Iyer-Wald entropy.

hep-th↗

arXiv2021

Well-posed formulation of Einstein-Maxwell effective field theory

We consider the well-posedness of the initial value problem for Einstein-Maxwell theory modified by higher derivative effective field theory corrections. Field redefinitions can be used to bring the leading parity-symmetric 4-derivative corrections to a form which gives second order equations of motion. We show that a recently introduced "modified harmonic" gauge condition can be used to obtain a formulation of these theories which admits a well-posed initial value problem when the higher derivative corrections to the equations of motion are small.

gr-qc↗

arXiv2021

Effective field theory and classical equations of motion

Given a theory containing both heavy and light fields (the UV theory), a standard procedure is to integrate out the heavy field to obtain an effective field theory (EFT) for the light fields. Typically the EFT equations of motion consist of an expansion involving higher and higher derivatives of the fields, whose truncation at any finite order may not be well-posed. In this paper we address the question of how to make sense of the EFT equations of motion, and whether they provide a good approximation to the classical UV theory. We propose an approach to solving EFTs which leads to a well-posedness statement. For a particular choice of UV theory we rigorously derive the corresponding EFT and show that a large class of classical solutions to the UV theory are well approximated by EFT solutions. We also consider solutions of the UV theory which are not well approximated by EFT solutions and demonstrate that these are close, in an averaged sense, to solutions of a modified EFT.

hep-th↗

arXiv2021

Causality in gravitational theories with second order equations of motion

This paper considers diffeomorphism invariant theories of gravity coupled to matter, with second order equations of motion. This includes Einstein-Maxwell and Einstein-scalar field theory with (after field redefinitions) the most general parity-symmetric four-derivative effective field theory corrections. A gauge-invariant approach is used to study the characteristics associated to the physical degrees of freedom in an arbitrary background solution. The symmetries of the principal symbol arising from diffeomorphism invariance and the action principle are determined. For gravity coupled to a single scalar field (i.e. a Horndeski theory) it is shown that causality is governed by a characteristic polynomial of degree $6$ which factorises into a product of quadratic and quartic polynomials. The former is defined in terms of an "effective metric" and is associated with a "purely gravitational" polarisation, whereas the latter generically involves a mixture of gravitational and scalar field polarisations. The "fastest" degrees of freedom are associated with the quartic polynomial, which defines a surface analogous to the Fresnel surface in crystal optics. In contrast with optics, this surface is generically non-singular except on certain surfaces in spacetime. It is shown that a Killing horizon is an example of such a surface. It is also shown that a Killing horizon satisfies the zeroth law of black hole mechanics. The characteristic polynomial defines a cone in the cotangent space and a dual cone in the tangent space. The latter is used to define basic notions of causality and to provide a definition of a dynamical black hole in these theories.

gr-qc↗

arXiv2020

Well-posed formulation of Lovelock and Horndeski theories

We study the initial value problem for Lovelock and Horndeski theories of gravity. We show that the equations of motion of these theories can be written in a form that, at weak coupling, is strongly hyperbolic and therefore admits a well-posed initial value problem. This is achieved by introducing a new class of "modified harmonic" gauges for general relativity.

gr-qc↗

arXiv2020

Well-posed formulation of scalar-tensor effective field theory

Effective field theory provides a way of parameterizing strong-field deviations from General Relativity that might be observable in the gravitational waves emitted in a black hole merger. To perform numerical simulations of mergers in such theories it is necessary that the equations be written in a form that admits a well-posed initial value formulation. We study gravity coupled to a scalar field including the leading (4-derivative) effective field theory corrections. We introduce a new class of "modified harmonic" gauges and gauge-fixed equations of motion, such that, at weak coupling, the equations are strongly hyperbolic and therefore admit a well-posed initial value formulation.

gr-qc↗