888 research outputs found
Regularization of fields for self-force problems in curved spacetime: foundations and a time-domain application
We propose an approach for the calculation of self-forces, energy fluxes and
waveforms arising from moving point charges in curved spacetimes. As opposed to
mode-sum schemes that regularize the self-force derived from the singular
retarded field, this approach regularizes the retarded field itself. The
singular part of the retarded field is first analytically identified and
removed, yielding a finite, differentiable remainder from which the self-force
is easily calculated. This regular remainder solves a wave equation which
enjoys the benefit of having a non-singular source. Solving this wave equation
for the remainder completely avoids the calculation of the singular retarded
field along with the attendant difficulties associated with numerically
modeling a delta function source. From this differentiable remainder one may
compute the self-force, the energy flux, and also a waveform which reflects the
effects of the self-force. As a test of principle, we implement this method
using a 4th-order (1+1) code, and calculate the self-force for the simple case
of a scalar charge moving in a circular orbit around a Schwarzschild black
hole. We achieve agreement with frequency-domain results to ~ 0.1% or better.Comment: 15 pages, 12 figures, 1 table. More figures, extended summar
Rotating black holes in three-dimensional Ho\v{r}ava gravity
We study black holes in the infrared sector of three-dimensional Ho\v{r}ava
gravity. It is shown that black hole solutions with anti-de Sitter asymptotics
are admissible only in the sector of the theory in which the scalar degree of
freedom propagates infinitely fast. We derive the most general class of
stationary, circularly symmetric, asymptotically anti-de Sitter black hole
solutions. We also show that the theory admits black hole solutions with de
Sitter and flat asymptotics, unlike three-dimensional general relativity. For
all these cases, universal horizons may or may not exist depending on the
choice of parameters. Solutions with de Sitter asymptotics can have universal
horizons that lie beyond the de Sitter horizon.Comment: 16 pages, 9 figures, final published versio
Self-force with (3+1) codes: a primer for numerical relativists
Prescriptions for numerical self-force calculations have traditionally been
designed for frequency-domain or (1+1) time-domain codes which employ a mode
decomposition to facilitate in carrying out a delicate regularization scheme.
This has prevented self-force analyses from benefiting from the powerful suite
of tools developed and used by numerical relativists for simulations of the
evolution of comparable-mass black hole binaries. In this work, we revisit a
previously-introduced (3+1) method for self-force calculations, and demonstrate
its viability by applying it to the test case of a scalar charge moving in a
circular orbit around a Schwarzschild black hole. Two (3+1) codes originally
developed for numerical relativity applications were independently employed,
and in each we were able to compute the two independent components of the
self-force and the energy flux correctly to within . We also demonstrate
consistency between -component of the self-force and the scalar energy flux.
Our results constitute the first successful calculation of a self-force in a
(3+1) framework, and thus open opportunities for the numerical relativity
community in self-force analyses and the perturbative modeling of
extreme-mass-ratio inspirals.Comment: 23 pages, 13 figure
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