Session J11: Theoretical Gravity

Relativistic theory of tidal Love numbers

In Newtonian gravitational theory, a tidal Love number $k_l$ relates the mass multipole moment $Q_l$ created on a spherical body to the applied tidal field $E_l$; the integer $l \geq 2$ is the multipole order. The relation is of the form $Q_l = k_l a^{2l+1} E_l$, where $a$ is the radius of the unperturbed body. The Love number is dimensionless, and it encodes information about the body's internal structure. In this talk we present a relativistic theory of Love numbers, which applies to compact bodies with strong internal gravity; our theory extends and completes the previous work of Flanagan and Hinderer (2007) and Hinderer (2008). We consider a spherical body deformed by an external tidal field, and we provide precise and meaningful definitions for electric-type and magnetic-type Love numbers; and we compute these numbers for polytropic equations of state. The theory applies to black holes as well, and we find that the relativistic Love numbers of a nonrotating black hole are all zero.   

How do Black Holes Rotate in Parity-Violating Gravity?

General Relativity is a parity-preserving theory, but quantum gravitational theories require that parity be violated, for example through the Green-Schwarz mechanism in String Theory. The unique, leading-order effective theory that captures such parity violation is Chern-Simons modified gravity. In this modified theory, however, the Kerr metric is not a solution, and an exact, strong-field solution that represents rotating black holes is still lacking. In this talk, we summarize the status of the search for rotating black hole solutions in Chern-Simons modified gravity and present some preliminary results of numerical investigations that might lead to the missing solution.   

Vector models of gravitational Lorentz breaking

Dynamical Lorentz symmetry breaking can occur when the dynamics of a tensor field cause it to take on a non-zero expectation value \textit{in vacuo}, thereby providing one or more ``preferred directions'' in spacetime. Couplings between such fields and spacetime curvature will then affect the dynamics of the metric, leading to interesting gravitational effects. Bailey \& Kosteleck\'{y} (2006) developed a PPN-like formalism that, under certain assumptions concerning the field's couplings and stress-energy, allows for the analysis of gravitational effects in the presence of Lorentz symmetry breaking. We systematically investigate which vector models of Lorentz breaking can be successfully analyzed under the Bailey-Kosteleck\'{y} formalism. Implications for the gravitational analysis of specific Lorentz-breaking vector models, including Bekenstein's ``TeVeS'' and Carroll \textit{et al.}'s ``sigma-model {\ae}ther'', are discussed.   

Cosmological Tests of General Relativity/

A detailed analysis of gravitational slip, a post-general relativity cosmological parameter characterizing the degree of departure of the laws of gravitation from general relativity on cosmological scales, is presented. This phenomenological approach assumes that cosmic acceleration is due to new gravitational effects; the amount of spacetime curvature produced per unit mass is changed in such a way that a Universe containing only matter and radiation begins to accelerate as if under the influence of a cosmological constant. Changes in the law of gravitation are further manifest in the behavior of the inhomogeneous gravitational field, as reflected in the cosmic microwave background, weak lensing, and evolution of large-scale structure.   

Spacetimes and orbits of Bumpy Black Holes

Observations show the existence of many extremely compact, massive objects which are generally believed to be black holes. Precise observations have the potential to determine if these black hole candidates have the multipolar structure predicted by general relativity. Collins and Hughes proposed analyzing these systems by considering ``bumpy black holes'': objects that are almost, but not quite, black holes. In this talk we extend the work of Collins and Hughes. We describe how to add bumps to a Kerr background that correspond to modifying in a prescribed way the multipolar structure of the black hole spacetime. We describe the effect of the bumps by describing how the frequencies of motion change using Hamilton-Jacobi techniques.   

Characterizing particle orbits in general stationary axis-symmetric vacuum spacetimes

Determining the nature of a central compact object in a highly curved spacetime, requires detailed knowledge of the orbital trajectories of probe particles within this spacetime. The Carter Constant fully characterizes the geodesic structure of the Kerr spacetimes making the computation of observational waveforms for extreme mass ratio inspirals (EMRI's) possible. In more general stationary axis-symmetric vacuum (SAV) spacetimes not much is known. The first results of a method to systematically check for higher order Killing tensors which may describe orbital motion in general SAV spacetimes are presented.   

Finding Fields and Self-Force in a Gauge Appropriate to Separable Wave Equations

Gravitational waves from the inspiral of a stellar-size black hole to a supermassive black hole can be accurately approximated by a point particle moving in a Kerr background. A procedure for finding the renormalized self-force from the Tuekolsky equation \footnote{Teukolsky, S. A., Astrophys. J., \textbf{185}, 635-647, (1973)} has been outlined in the separate paper \footnote{T.~S.~Keidl, J.~L.~Friedman, A.~G.~Wiseman, Phys. Rev. D, in press; gr-qc0611072}. This talk focuses on analytic work developed in this formalism and incorporating the $l=0$ and $l=1$ parts of the self-force. The self-force is calculated from either the renormalized spin $+2$ or the spin $-2$ Weyl scalar ($\psi_0$ or $\psi_4$). The self-force is can then be calculated algebraically from either renormalized Weyl scalar.   

Self-force for a particle in circular orbit around Schwarzschild black hole.

This talk reports the successful computation of the self-force in the radiation gauge for a particle orbiting a Schwarzschild black hole. We find the renormalized spin-2 Weyl scalar for a particle in circular orbit in Schwarzschild geometry, subtracting from the retarded field an expression for the singular field to subleading order. Remarkably, only one term in a lengthy expression for the singular field contributes at this order, and that term coincides up to an overall factor (associated with a boost) with the perturbed Weyl scalar of a static field. We use a numerical matching procedure to remove the singular field to one additional order. Finally, following the procedure outlined in KFW (Phys Rev D, 75, 2007) we calculate the renormalized Hertz potential (from the renormalized Weyl scalar), from which one finds the renormalized perturbed metric and hence the conservative part of the self-force.   

Relativistic Images as Probe of Alternative Gravity

In this presentation I consider the effects of RS-braneworld geometry on gravitational lensing observables. Findings show that the resolution needed to distinguish RS lensing from Schwarzschild lensing is expected to be obtainable in the next generation of VLBI arrays, but the expected magnitudes of these images present great challenges. Several approaches to finding observables are explored: 1) A straightforward calculation of relativistic image properties in several proposed RS gravity metrics. 2) Femtolensing of gamma-ray bursts from tiny braneworld primordial black holes, including effects from microlensing of relativistic images. Results are obtained using numerical solutions of the Virbhadra- Ellis lens equation and are compared with results obtained from approximations of the lens equation frequently used in the literature, confirming the validity of the approximations.