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Ted Jacobson

Publications and source records attributed to Ted Jacobson.

At least 73 records · Page 4Linked to original sources
arXiv2011

Cosmic alignment of the aether

In Einstein-aether theory and Horava gravity, a timelike unit vector is coupled to the spacetime metric. It has previously been shown that in an exponentially expanding homogeneous, isotropic background, small perturbations of the vector relax back to the isotropic frame. Here we investigate large deviations from isotropy, maintaining homogeneity. We find that, for generic values of the coupling constants, the aether and metric relax to the isotropic configuration if the initial aether hyperbolic boost angle and its time derivative in units of the cosmological constant are less than something of order unity. For larger angles or angle derivatives, the behavior is strongly dependent on the values of the coupling constants. Generally there is runaway behavior, in which the anisotropy increases with time, and/or singularities occur.

gr-qc↗
arXiv2010

Extended Horava gravity and Einstein-aether theory

Einstein-aether theory is general relativity coupled to a dynamical, unit timelike vector. If this vector is restricted in the action to be hypersurface orthogonal, the theory is identical to the IR limit of the extension of Horava gravity proposed by Blas, Pujolàs and Sibiryakov. Hypersurface orthogonal solutions of Einstein-aether theory are solutions to the IR limit of this theory, hence numerous results already obtained for Einstein-aether theory carry over.

hep-th↗
arXiv2010

Might black holes reveal their inner secrets?

Black holes harbor a spacetime singularity of infinite curvature, where classical spacetime physics breaks down, and current theory cannot predict what will happen. However, the singularity is invisible from the outside because strong gravity traps all signals, even light, behind an event horizon. In this essay we discuss whether it might be possible to destroy the horizon, if a body is tossed into the black hole so as to make it spin faster and/or have more charge than a certain limit. It turns out that one could expose a "naked" singularity if effects of the body's own gravity can be neglected. We suspect however that such neglect is unjustified.

gr-qc↗
arXiv2010

Destroying black holes with test bodies

If a black hole can accrete a body whose spin or charge would send the black hole parameters over the extremal limit, then a naked singularity would presumably form, in violation of the cosmic censorship conjecture. We review some previous results on testing cosmic censorship in this way using the test body approximation, focusing mostly on the case of neutral black holes. Under certain conditions a black hole can indeed be over-spun or over-charged in this approximation, hence radiative and self-force effects must be taken into account to further test cosmic censorship.

gr-qc↗
arXiv2010

Black Holes in Einstein-Aether Theory

We study black hole solutions in general relativity coupled to a unit timelike vector field dubbed the "aether". To be causally isolated a black hole interior must trap matter fields as well as all aether and metric modes. The theory possesses spin-0, spin-1, and spin-2 modes whose speeds depend on four coupling coefficients. We find that the full three-parameter family of local spherically symmetric static solutions is always regular at a metric horizon, but only a two-parameter subset is regular at a spin-0 horizon. Asymptotic flatness imposes another condition, leaving a one-parameter family of regular black holes. These solutions are compared to the Schwarzschild solution using numerical integration for a special class of coupling coefficients. They are very close to Schwarzschild outside the horizon for a wide range of couplings, and have a spacelike singularity inside, but differ inside quantitatively. Some quantities constructed from the metric and aether oscillate in the interior as the singularity is approached. The aether is at rest at spatial infinity and flows into the black hole, but differs significantly from the the 4-velocity of freely-falling geodesics.

gr-qc↗
arXiv2010

Black Hole Thermodynamics and Lorentz Symmetry

Recent developments point to a breakdown in the generalized second law of thermodynamics for theories with Lorentz symmetry violation. It appears possible to construct a perpetual motion machine of the second kind in such theories, using a black hole to catalyze the conversion of heat to work. Here we describe and extend the arguments leading to that conclusion. We suggest the inference that local Lorentz symmetry may be an emergent property of the macroscopic world with origins in a microscopic second law of causal horizon thermodynamics.

hep-th↗
arXiv2010

Spinning Black Holes as Particle Accelerators

It has recently been pointed out that particles falling freely from rest at infinity outside a Kerr black hole can in principle collide with arbitrarily high center of mass energy in the limiting case of maximal black hole spin. Here we aim to elucidate the mechanism for this fascinating result, and to point out its practical limitations, which imply that ultra-energetic collisions cannot occur near black holes in nature.

gr-qc↗
arXiv2009

Spherical Solutions in Einstein-Aether Theory: Static Aether and Stars

The time independent spherically symmetric solutions of General Relativity (GR) coupled to a dynamical unit timelike vector are studied. We find there is a three-parameter family of solutions with this symmetry. Imposing asymptotic flatness restricts to two parameters, and requiring that the aether be aligned with the timelike Killing field further restricts to one parameter, the total mass. These "static aether" solutions are given analytically up to solution of a transcendental equation. The positive mass solutions have spatial geometry with a minimal area 2-sphere, inside of which the area diverges at a curvature singularity occurring at an extremal Killing horizon that lies at a finite affine parameter along a radial null geodesic. Regular perfect fluid star solutions are shown to exist with static aether exteriors, and the range of stability for constant density stars is identified.

gr-qc↗
arXiv2009

Neutron stars in Einstein-aether theory

As current and future experiments probe strong gravitational regimes around neutron stars and black holes, it is desirable to have theoretically sound alternatives to general relativity against which to test observations. Here we study the consequences of one such generalization, Einstein-aether theory, for the properties of non-rotating neutron stars. This theory has a parameter range that satisfies all current weak-field tests. We find that within this range it leads to lower maximum neutron star masses, as well as larger surface redshifts at a particular mass, for a given nuclear equation of state. For non-rotating black holes and neutron stars, the innermost stable circular orbit is only slightly modified in this theory.

gr-qc↗
arXiv2009

Over-spinning a black hole with a test body

It has long been known that a maximally spinning black hole can not be over-spun by tossing in a test body. Here we show that if instead the black hole starts out with below maximal spin, then indeed over-spinning can be achieved when adding either orbital or spin angular momentum. We find that requirements on the size and internal structure of the test body can be met as well. Our analysis neglects radiative and self-force effects,which may prevent the over-spinning.

gr-qc↗
arXiv2009

String dynamics and ejection along the axis of a spinning black hole

Relativistic current carrying strings moving axisymmetrically on the background of a Kerr black hole are studied. The boundaries and possible types of motion of a string with a given energy and current are found. Regions of parameters for which the string falls into the black hole, or is trapped in a toroidal volume, or can escape to infinity, are identified, and representative trajectories are examined by numerical integration, illustrating various interesting behaviors. In particular, we find that a string can start out at rest near the equatorial plane and, after bouncing around, be ejected out along the axis, some of its internal (elastic or rotational kinetic) energy having been transformed into translational kinetic energy. The resulting velocity can be an order unity fraction of the speed of light. This process results from the presence of an outer tension barrier and an inner angular momentum barrier that are deformed by the gravitational field. We speculatively discuss the possible astrophysical significance of this mechanism as a means of launching a collimated jet of MHD plasma flux tubes along the spin axis of a gravitating system fed by an accretion disk.

gr-qc↗
arXiv2009

Slices of the Kerr ergosurface

The intrinsic geometry of the Kerr ergosurface on constant Boyer-Lindquist (BL), Kerr, and Doran time slices is characterized. Unlike the BL slice, which had been previously studied, the other slices (i) do not have conical singularities at the poles (except the Doran slice in the extremal limit), (ii) have finite polar circumference in the extremal limit, and (iii) for sufficiently large spin parameter fail to be isometrically embeddable as a surface of revolution above some latitude. The Doran slice develops an embeddable polar cap for spin parameters greater than about 0.96.

gr-qc↗
arXiv2008

Horizon surface gravity as 2d geodesic expansion

The surface gravity of any Killing horizon, in any spacetime dimension, can be interpreted as a local, two-dimensional expansion rate seen by freely falling observers when they cross the horizon. Any two-dimensional congruence of geodesics invariant under the Killing flow can be used to define this expansion, provided that the observers have unit Killing energy.

gr-qc↗
arXiv2008

Einstein-aether gravity: a status report

This paper reviews the theory, phenomenology, and observational constraints on the coupling parameters of Einstein-aether gravity, i.e. General Relativity coupled to a dynamical unit timelike vector field. A discussion of open questions concerning both phenomenology and fundamental issues is included.

gr-qc↗
arXiv2007

When is g_{tt} g_{rr} = -1?

The Schwarzschild metric, its Reissner-Nordstrom-de Sitter generalizations to higher dimensions, and some further generalizations all share the feature that g_{tt} g_{rr}=-1 in Schwarzschild-like coordinates. In this pedagogical note we trace this feature to the condition that the Ricci tensor (and stress-energy tensor in a solution to Einstein's equation) has vanishing radial null-null component, i.e. is proportional to the metric in the t-r subspace. We also show this condition holds if and only if the area-radius coordinate is an affine parameter on the radial null geodesics.

gr-qc↗
arXiv2007

Renormalization and black hole entropy in Loop Quantum Gravity

Microscopic state counting for a black hole in Loop Quantum Gravity yields a result proportional to horizon area, and inversely proportional to Newton's constant and the Immirzi parameter. It is argued here that before this result can be compared to the Bekenstein-Hawking entropy of a macroscopic black hole, the scale dependence of both Newton's constant and the area must be accounted for. The two entropies could then agree for any value of the Immirzi parameter, if a certain renormalization property holds.

gr-qc↗
arXiv2007

Black hole entanglement entropy regularized in a freely falling frame

We compute the black hole horizon entanglement entropy S_E for a massless scalar field, first with a hard cutoff and then with high frequency dispersion, both imposed in a frame that falls freely across the horizon. Using WKB methods, we find that S_E is finite for a hard cutoff or super-luminal dispersion, because the mode oscillations do not diverge at the horizon and the contribution of high transverse momenta is cut off by the angular momentum barrier. For sub-luminal dispersion the entropy depends on the behavior at arbitrarily high transverse momenta. In all cases it scales with the horizon area. For the hard cutoff it is linear in the cutoff, rather than quadratic. This discrepancy from the familiar result arises from the difference between the free-fall frame and the static frame in which a cutoff is usually imposed. In the super-luminal case the entropy scales with a fractional power of the cutoff that depends on the index of the dispersion relation. Implications for the possible relation between regularized entanglement entropy and the Bekenstein-Hawking entropy are discussed.

hep-th↗