Gravitational Wave Forms for Two- and Three-Body Gravitating Systems

In this paper we start a systematic investigation of applying an adaptive finite element method to the Einstein equations, especially binary compact object simulations. To our knowledge, this is the first study on this topic. Puncture type initial data are solved with the adaptive finite element method. The numerical scheme proposed in the current work can be straightforwardly extended to the general type of initial data of the Einstein equations. The Parallel Hierarchical Grid library and the existing numerical relativity code AMSS-NCKU are used to develop the adaptive finite element Einstein solver. In the unsmooth toy model problem, the adaptive mesh refinement operation can catch the unsmooth region efficiently. The numerical solution deviates the exact solution by an error less than 10"5. In the binary black hole problem, our solution is consistent with the one gotten by the TwoPuncture code which uses a pseudospectral method. As we expected, the solution gotten by the finite element method is less accurate than that gotten by the spectral method. But the relative error distributes almost uniformly. The adaptive mesh refinement method is quite efficient and it does not waste computational effort. Our finite element code is more flexible than the TwoPuncture code. It can be used to treat other general initial data problems such as the three black holes problem, besides the binary black hole problem. We test one typical three black holes problem also. In all of the test cases, our adaptive finite element code works quite well.

Section: Initial Data For Three Punctured Black Holesmentioning

confidence: 99%

Binary black hole simulation with an adaptive finite element method: Solving the Einstein constraint equations

Cao

2015

“…In the wave zone, we also have [73], 50) where N k denotes the unit vector along the direction between the source and the observer. Then, inserting the above expressions into Eq.…”

Section: A Polarizations Of Gravitational Waves In Einstein-aether Tmentioning

confidence: 99%

Gravitational waveforms, polarizations, response functions, and energy losses of triple systems in Einstein-aether theory

Lin¹,

Zhao²,

Zhang³

et al. 2019

Gravitationally bound hierarchies containing three or more components are very common in our Universe. In this paper we study periodic gravitational wave (GW) form, their polarizations, response function, its Fourier transform, and energy loss rate of a triple system through three different channels of radiation, the scalar, vector and tensor modes, in Einstein-aether theory of gravity. The theory violates locally the Lorentz symmetry, and yet satisfies all the theoretical and observational constraints by properly choosing its four coupling constants ci's. In particular, in the weak-field approximations and with the recently obtained constraints of the theory, we first analyze the energy loss rate of a binary system, and find that the dipole contributions from the scalar and vector modes could be of the order of O (c14) O (GN m/d) 2 , where c14 (≡ c1 + c4) is constrained to c14 O 10 −5 by current observations, and GN , m and d are, respectively, the Newtonian constant, mass and size of the source. On the other hand, the "strong-field" effects for a binary system of neutron stars are about six orders lower than that of GR. So, in this paper we ignore these "strong-field" effects and first develop the general formulas to the lowest post-Newtonian order, by taking the coupling of the aether field with matter into account. Within this approximation, we find that the scalar breather mode and the scalar longitudinal mode are all suppressed by a factor of O (c14) with respect to the transverse-traceless modes (h+ and h×), while the vectorial modes (hX and hY ) are suppressed by a factor of c13 O 10 −15 . Applying the general formulas to a triple system with periodic orbits, we find that the corresponding GW form, response function, and its Fourier transform depend sensitively on the configuration of the triple system, their orientation with respect to the detectors, and the binding energies of the three compact bodies.

“…Indeed, the formation of the binary black hole shadow mentioned above is the problem of the dynamics of massless particles. On the other hand, the dynamics of massive particles in a binary black hole system has been discussed in the contexts of gravitational wave radiation induced by a third body effect [15][16][17][18] and the formation of multiple accretion disks [19,20]. In these phenomena, the sequence of stable circular orbits is crucial, and in particular, the innermost stable circular orbit (ISCO) plays a key role because it is expected to be the inner edge of an accretion disk [21], and also an inspiralling compact binary transits into the merging phase there [22,23].…”

Section: Introductionmentioning

confidence: 99%

Innermost stable circular orbits in the Majumdar-Papapetrou dihole spacetime

Nakashi

Igata

2019

We investigate the positions of stable circular massive particle orbits in the Majumdar-Papapetrou dihole spacetime with equal mass. In terms of qualitative differences of their sequences, we classify the dihole separation into five ranges and find four critical values as the boundaries. When the separation is relatively large, the sequence on the symmetric plane bifurcates, and furthermore, they extend to each innermost stable circular orbit in the vicinity of each black hole. In a certain separation range, the sequence on the symmetric plane separates into two parts. On the basis of this phenomenon, we discuss the formation of double accretion disks with a common center. Finally, we clarify the dependence of the radii of marginally stable circular orbits and innermost stable circular orbits on the separation parameter. We find a discontinuous transition of the innermost stable circular orbit radius. We also find the separation range at which the radius of the innermost stable circular orbit can be smaller than that of the stable circular photon orbit. * Electronic address: nakashi@rikkyo.ac.jp † Electronic address: igata@rikkyo.ac.jp