Extreme Mass Ratio Binary: Radiation reaction and gravitational waveform

For a successful detection of gravitational waves by LISA, it is essential to construct theoretical waveforms in a reliable manner. We discuss gravitational waves from an extreme mass ratio binary system which is expected to be a promising target of the LISA project. The extreme mass ratio binary is a binary system of a supermassive black hole and a stellar mass compact object. As the supermassive black hole dominates the gravitational field of the system, we suppose that the system might be well approximated by a metric perturbation of a Kerr black hole. We discuss a recent theoretical progress in calculating the waveforms from such a system.Comment: Classical and Quantum Gravity 22 (2005) S375-S379, Proceedings for 5th International LISA Symposiu

Modulation of the gravitational waveform by the effect of radiation reaction

When we calculate gravitational waveforms from extreme-mass-ratio inspirals by metric perturbation, it is a common strategy to use the adiabatic approximation. Under that approximation, we first calculate the linear metric perturbation induced by geodesics orbiting a black hole, then we calculate the adiabatic evolution of the parameters of geodesics due to the radiation reaction effect through the calculation of the self-force. This procedure is considered to be reasonable, however, there is no direct proof that it can actually produce the correct waveform we would observe. In this paper, we study the formal expression of the second order metric perturbation and show that it can be expressed as the linear metric perturbation modulated by the adiabatic evolution of the geodesic. This evidence supports the assumption that the adiabatic approximation can produce the correct waveform, and that the adiabatic expansion we propose in Ref. [Y. Mino, Prog. Theor. Phys. 115, 43 (2006); Y. Mino, Prog. Theor. Phys. 113, 733 (2005); Y. Mino and R. Price (unpublished).] is an appropriate perturbation expansion for studying the radiation reaction effect on the gravitational waveform

Adiabatic Expansion for Metric Perturbation and the condition to solve the Gauge Problem for Gravitational Radiation Reaction Problem

We examine the adiabatic approximation in the study of a relativistic two-body problem with the gravitational radiation reaction. We recently pointed out that the usual metric perturbation scheme using a perturbation of the stress-energy tensor may not be appropriate for study of the dissipative dynamics of the bodies due to the radiation reaction. We recently proposed a possible approach to solve this problem with a linear black hole perturbation. This paper proposes a non-linear generalization of that method for a general application of this problem. We show that, under a specific gauge condition, the method actually allows us to avoid the gauge problem.Comment: accepted by Progress of Theoretical Physic

From the self-force problem to the Radiation reaction formula

We review a recent theoretical progress in the so-called self-force problem of a general relativistic two-body system. Although a two-body system in Newtonian gravity is a very simple problem, some fundamental issues are involved in relativistic gravity. Besides, because of recent projects for gravitational wave detection, it comes to be possible to see those phenomena directly via gravitational waves, and the self-force problem becomes one of urgent and highly-motivated problems in general relativity. Roughly speaking, there are two approaches to investigate this problem; the so-called post-Newtonian approximation, and a black hole perturbation. In this paper, we review a theoretical progress in the self-force problem using a black hole perturbation. Although the self-force problem seems to be just a problem to calculate a self-force, we discuss that the real problem is to define a gauge invariant concept of a motion in a gauge dependent metric perturbation.Comment: a special issue for Classical and Quantum Gravity, a review article of Capra Ranch Meeting

Perturbative Approach to an orbital evolution around a Supermassive black hole

A charge-free, point particle of infinitesimal mass orbiting a Kerr black hole is known to move along a geodesic. When the particle has a finite mass or charge, it emits radiation which carries away orbital energy and angular momentum, and the orbit deviates from a geodesic. In this paper we assume that the deviation is small and show that the half-advanced minus half-retarded field surprisingly provides the correct radiation reaction force, in a time-averaged sense, and determines the orbit of the particle.Comment: accepted for publication in the Physical Revie

Financial integration and volatility in a two-country world

This paper investigates a two-country model of capital accumulation with country-specific production externalities. The main concern of our discussion is to explore the presence of equilibrium indeterminacy in an open-economy setting. In contrast to the existing studies on equilibrium indeterminacy in small-open economies, the present paper demonstrates that opening up international trade and financial interactions between two counties does not necessarily enhance the possibility of indeterminacy of equilibrium. It is shown that the results depend heavily upon not only on the degree of external increasing returns but also on the preference structures.Financial integration, Two-country growth model, Equilibrium determinacy, Preference structure

Monetary Expansion and Converging Speed in a Growing Economy

This paper explores the effect of monetary policy on the speed of convergence. Using a neoclassical monetary growth model with a cash-in-advance constraint, we conduct numerical evaluation of the effect of changes in the growth rate of money supply on the converging speed of the economy. We find that, in contrast to fiscal actions, a change in monetary policy may produce little impact on the converging speed. This result indicates that the growth effect of inflation established in the theoretical models of money and growth would be extremely small, if we evaluated it quantitatively.monetary growth, speed of convergence, neoclassical growth model

On Time Consistency in Stackelberg Differential Games

This paper explores a class of Stackelberg differential games in which the open-loop strategies of the leader satisfies time consistency. We show that in this class of games the open-loop equilibrium coincides with the corresponding feedback equilibrium. The analytical framework used in this paper involves the models examined by the several recent contributions to the time consistency issue as special cases.Stackelberg differential game, open-loop equilibrium, feedback equilibrium, time consistency

Consumption Externalities and Capital Accumulation in an Overlapping Generations Economy

This paper extends the standard overlapping generations model of capital accumulation by introducing consumption externalities. It is assumed that each generation's felicity depends on the social level of benchmark consumption as well as on its own consumption. Since the benchmark consumption is represented by the average consumption of all agents, the contemporaneous consumption externalities are determined by both intragenerational and intergenerational interactions among the consumers. Given this setting, we show that even in a simple model with a logarithmic utility function, the presence of consumption externalities may significantly affect the dynamic behavior and steady-state characterization of the economy. We also reveal that the same conclusion holds in an endogenous growth model in which production externalities sustain continuing growth.overlapping generations, benchmark consumption, intergenerational externalities, intragenerational externalities