Exponential Metric Fields

TL;DR

This paper proposes a method to construct gravitational templates with exponential non-linearities, aiming to test Einstein's theories beyond first order using LISA's capabilities.

Contribution

It introduces a novel approach to model metric fields with exponential non-linear terms, extending gravitational theory testing beyond first order.

Findings

First-order Newtonian limit matches General Relativity

Method allows testing second-order gravitational effects

Potential to identify non-linear features of gravity with LISA

Abstract

The Laser Interferometer Space Antenna (LISA) mission will use advanced technologies to achieve its science goals: the direct detection of gravitational waves, the observation of signals from compact (small and dense) stars as they spiral into black holes, the study of the role of massive black holes in galaxy evolution, the search for gravitational wave emission from the early Universe. The gravitational red-shift, the advance of the perihelion of Mercury, deflection of light and the time delay of radar signals are the classical tests in the first order of General Relativity (GR). However, LISA can possibly test Einstein's theories in the second order and perhaps, it will show some particular feature of non-linearity of gravitational interaction. In the present work we are seeking a method to construct theoretical templates that limit in the first order the tensorial structure of some metric fields, thus the non-linear terms are given by exponential functions of gravitational strength. The Newtonian limit obtained here, in the first order, is equivalent to GR.