59 research outputs found
A possible failure of determinism in general relativity
Is the future predictable? If we know the initial state of a system exactly, then do the laws of physics determine its state arbitrarily far into the future? In Newtonian mechanics, the answer is yes. Similarly in electromagnetism: if one knows the initial state of the electric and magnetic fields exactly, then Maxwellâs equations determine their state at any later time. In quantum mechanics, if the initial wave function is known exactly, then Schrödingerâs equation can be used to predict the wave function at any later time. However, new research by Vitor Cardoso from the University of Lisbon, Portugal, and colleagues [1] suggests that this predictability of the laws of physics can fail in general relativity. The researchers find that it might be possible for a star that undergoes gravitational collapse to form a black hole containing a region in which physics cannot be predicted from the initial state of the star
Classical and thermodynamic stability of black branes
It is argued that many non-extremal black branes exhibit a classical
Gregory-Laflamme instability if, and only if, they are locally
thermodynamically unstable. For some black branes, the Gregory-Laflamme
instability must therefore disappear near extremality. For the black -branes
of the type II supergravity theories, the Gregory-Laflamme instability
disappears near extremality for but persists all the way down to
extremality for (the black D3-brane is not covered by the analysis of
this paper). This implies that the instability also vanishes for the
near-extremal black M2 and M5-brane solutions.This work was supported by the Fundação para a CiĂȘncia e Tecnologia (Portugal), throught the grant SFRH/BD/22211/2005, and, in its final stages, by the Cambridge Philosophical Society
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 âeffective metricâ and is associated with a âpurely gravitationalâ polarisation, whereas the latter generically involves a mixture of gravitational and scalar field polarisations. The âfastestâ 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.This work was supported by STFC grant no. ST/T000694/1
Evanescent ergosurfaces and ambipolar hyperkÀhler metrics
A supersymmetric solution of 5d supergravity may admit an `evanescent
ergosurface': a timelike hypersurface such that the canonical Killing vector
field is timelike everywhere except on this hypersurface. The hyperk\"ahler
`base space' of such a solution is `ambipolar', changing signature from
to across a hypersurface. In this paper, we determine how the
hyperk\"ahler structure must degenerate at the hypersurface in order for the 5d
solution to remain smooth. This leads us to a definition of an ambipolar
hyperk\"ahler manifold which generalizes the recently-defined notion of a
`folded' hyperk\"ahler manifold. We prove that such manifolds can be
constructed from `initial' data prescribed on the hypersurface. We present an
`initial value' construction of supersymmetric solutions of 5d supergravity, in
which such solutions are determined by data prescribed on a timelike
hypersurface, both for the generic case and for the case of an evanescent
ergosurface.This work was supported by ERC grant ERC-2011-StG 279363-HiDGR.This is the final version of the article. It first appeared from Springer via http://dx.doi.org/10.1007/JHEP04(2016)13
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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.HSR is supported by STFC Grants PHY-1504541 and
ST/P000681/1
Is there a breakdown of effective field theory at the horizon of an extremal black hole?
© 2017, The Author(s). Linear perturbations of extremal black holes exhibit the Aretakis instability, in which higher derivatives of a scalar field grow polynomially with time along the event horizon. This suggests that higher derivative corrections to the classical equations of motion may become large, indicating a breakdown of effective field theory at late time on the event horizon. We investigate whether or not this happens. For extremal Reissner-Nordstrom we argue that, for a large class of theories, general covariance ensures that the higher derivative corrections to the equations of motion appear only in combinations that remain small compared to two derivative terms so effective field theory remains valid. For extremal Kerr, the situation is more complicated since backreaction of the scalar field is not understood even in the two derivative theory. Nevertheless we argue that the effects of the higher derivative terms will be small compared to the two derivative terms as long as the spacetime remains close to extremal Kerr.SH is supported by the Blavatnik Postdoctoral Fellowship. SH is grateful to the Albert Einstein Institute, Potsdam for hospitality during the completion of this work. Part of this work was completed while HSR was a participant in the âGeometry and Relativityâ programme at the Erwin Schršodinger Institute, Vienna
Graviton time delay and a speed limit for small black holes in Einstein-Gauss-Bonnet theory
Camanho, Edelstein, Maldacena and Zhiboedov have shown that gravitons can
experience a negative Shapiro time delay, i.e. a time advance, in
Einstein-Gauss-Bonnet theory. They studied gravitons propagating in singular
"shock-wave" geometries. We study this effect for gravitons propagating in
smooth black hole spacetimes. For a small enough black hole, we find that
gravitons of appropriate polarisation, and small impact parameter, can
experience time advance. Such gravitons can also exhibit a deflection angle
less than , characteristic of a repulsive short-distance gravitational
interaction. We discuss problems with the suggestion that the time advance can
be used to build a "time machine". In particular, we argue that a small black
hole cannot be boosted to a speed arbitrarily close to the speed of light, as
would be required in such a construction.This work was supported by ERC grant No. ERC-2011-StG 279363-HiDGR and by an STFC studentshipThis is the final version of the article. It first appeared from Springer via http://dx.doi.org/10.1007/JHEP11(2015)10
On the local well-posedness of Lovelock and Horndeski theories
We investigate local well-posedness of the initial value problem for Lovelock and Horndeski theories of gravity. A necessary condition for local well-posedness is strong hyperbolicity of the equations of motion. Even weak hyperbolicity can fail for strong fields so we restrict to weak fields. The Einstein equation is known to be strongly hyperbolic in harmonic gauge so we study Lovelock theories in harmonic gauge. We show that the equation of motion is always weakly hyperbolic for weak fields but, in a generic weak-field background, it is not strongly hyperbolic. For Horndeski theories, we prove that, for weak fields, the equation of motion is always weakly hyperbolic in any generalized harmonic gauge. For some Horndeski theories there exists a generalized harmonic gauge for which the equation of motion is strongly hyperbolic in a weak-field background. This includes âk-essenceâ like theories. However, for more general Horndeski theories, there is no generalized harmonic gauge for which the equation of motion is strongly hyperbolic in a generic weak-field background. Our results show that the standard method used to establish local well-posedness of the Einstein equation does not extend to Lovelock or general Horndeski theories. This raises the possibility that these theories may not admit a well-posed initial value problem even for weak fields
Instability of supersymmetric microstate geometries
We investigate the classical stability of supersymmetric, asymptotically
flat, microstate geometries with five non-compact dimensions. Such geometries
admit an "evanescent ergosurface": a timelike hypersurface of infinite
redshift. On such a surface, there are null geodesics with zero energy relative
to infinity. These geodesics are stably trapped in the potential well near the
ergosurface. We present a heuristic argument indicating that this feature is
likely to lead to a nonlinear instability of these solutions. We argue that the
precursor of such an instability can be seen in the behaviour of linear
perturbations: nonlinear stability would require that all linear perturbations
decay sufficiently rapidly but the stable trapping implies that some linear
perturbation decay very slowly. We study this in detail for the most symmetric
microstate geometries. By constructing quasinormal modes of these geometries we
show that generic linear perturbations decay slower than any inverse power of
time.This work was supported by European Research Council grant ERC-2011-StG279363-HiDGR.This is the final version of the article. It first appeared from Springer via https://doi.org/10.1007/JHEP10(2016)03
Uniqueness of the Kerrâde Sitter Spacetime as an Algebraically Special Solution in Five Dimensions
We determine the most general solution of the five-dimensional vacuum
Einstein equation, allowing for a cosmological constant, with (i) a Weyl tensor
that is type II or more special in the classification of Coley et al., (ii) a
non-degenerate "optical matrix" encoding the expansion, rotation and shear of
the aligned null direction. The solution is specified by three parameters. It
is locally isometric to the 5d Kerr-de Sitter solution, or related to this
solution by analytic continuation or taking a limit. This is in contrast with
four dimensions, where there exist infinitely many solutions with properties
(i) and (ii).This work was supported by the European Research Council grant no. ERC-2011-StG 279363-HiDGR. G.B.F. is supported by CAPES grant no. 0252/11-5. M.G. is supported by Kingâs College, Cambridge.This is the final version of the article. It first appeared from Springer via http://dx.doi.org/10.1007/s00220-015-2447-
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