# Einstein and Beyond: A Critical Perspective on General Relativity

## Abstract

**:**

## 1. Introduction

## 2. Issues Warranting Attention: Mysteries of the Present with Roots in the Past

**Mach’s Principle:**Mach’s principle, akin to the equivalence principle, was the primary motivation and guiding principle for Einstein in the formulation of GR. (The name “Mach’s principle” was coined by Einstein for the general inspiration that he found in Mach’s works on mechanics [6], even though the principle itself was never formulated succinctly by Mach himself.) Though in the absence of a clear statement from Ernst Mach, there exist a number of formulations of Mach’s principle, in essence the principle advocates to shun all vestiges of the unobservable absolute space and time of Newton in favor of the directly observable background matter in the Universe, which determines its geometry and the inertia of an object.

**Equivalence Principle:**The equivalence principle—the physical foundation of any metric theory of gravitation—first expressed by Galileo and later reformulated by Newton, was assumed by Einstein as one of the defining principles of GR. According to the principle, one can choose a locally inertial coordinate system (LICS) (i.e., a freely-falling one) at any spacetime point in an arbitrary gravitational field such that within a sufficiently small region of the point in question, the laws of nature take the same form as in unaccelerated Cartesian coordinate systems in the absence of gravitation [8]. As has been mentioned earlier, this equivalence of gravitation and accelerated reference frames paved the way for the formulation of GR. Since the principle rests on the conviction that the equality of the gravitational and inertial mass is exact [8,9], one expects the same to hold in GR solutions. However, the inertial and the (active) gravitational mass have remained unequal in general. For instance, for the case of ${T}^{ik}$ representing a perfect fluid:

**and Gravitational Energy:**Appearing as the source term in Equation (1), ${T}^{ik}$ is expected to include all the inertial and gravitational aspects of matter, i.e., all the possible sources of gravitation. However, this requirement does not seem to be met on at least two counts. Firstly, ${T}^{ik}$ fails to support, in a general spacetime with no symmetries, an unambiguous definition of angular momentum, which is a fundamental and unavoidable characteristic of matter, as is witnessed from the subatomic to the galactic scales. While a meaningful notion of the angular momentum in GR always needs the introduction of some additional structure in the form of symmetries, quasi-symmetries, or some other background structure, it can be unambiguously defined only for isolated systems [10,11].

**Unphysical Solutions:**Since its very inception, GR started having observational support which substantiated the theory. Its predictions have been well-tested in the limit of the weak gravitational field in the solar system, and in the stronger fields present in the systems of binary pulsars. This has been done through two solutions—the Schwarzschild and Kerr solutions.

**Interior Solutions:**As mentioned earlier, GR successfully describes the gravitational field outside the Sun in terms of the Schwarzschild (exterior) and Kerr solutions. Nevertheless, the theory has not been that successful in describing the interior of a massive body.

**Dark Matter and Dark Energy:**Soon after formulating GR, Einstein applied his theory to model the Universe. At that time, Einstein believed in a static Universe, perhaps guided by his religious conviction that the Universe must be eternal and unchanging. As Equation (1) in its original form does not permit a static Universe, he inserted a term—the famous ‘cosmological constant Λ’ to force the equation to predict a static Universe. However, it was realized later that this gave an unstable Universe. It was then realized that a naive prediction of Equation (1) was an expanding Universe, which was subsequently found consistent with the observations. Realizing this, Einstein retracted the introduction of Λ terming it his “biggest blunder”.

**Horizon Problem:**Why does the cosmic microwave background (CMB) radiation look the same in all directions despite being emitted from regions of space failing to be causally connected? The size of the largest coherent region on the last scattering surface, in which the homogenizing signals passed at sound speed, can be measured in terms of the sound horizon. In the standard cosmology, this implies, however, that the CMB ought to exhibit large anisotropies (not isotropy) for angular scales of theorder of ${1}^{\circ}$ or larger—a result contrary to what is observed [8]. Hence, it seems that the isotropy of the CMB cannot be explained in terms of some physical process operating under the principle of causality in the standard paradigm.

**Flatness Problem:**In the standard cosmology, the total energy density ρ in the early Universe appears to be extremely fine-tuned to its critical value ${\rho}_{\mathrm{c}}=3{H}^{2}/(8\pi G$), which corresponds to a flat spatial geometry of the Universe, where H is the Hubble parameter. Since ρ departs rapidly from ${\rho}_{\mathrm{c}}$ over cosmic time, even a small deviation from this value would have had massive effects on the nature of the present Universe. For instance, the theory requires ρ at the Planck time to be within one part in ${10}^{57}$ of ${\rho}_{\mathrm{c}}$ in order to meet the observed uncertainties in ρ at present! That is, the Universe was almost flat just after the Big Bang—but how?

## 3. A New Perspective on Gravity

#### 3.1. Revisiting Mach’s Principle

**Postulate:**

#### 3.2. Fields without ${T}^{ik}$: An Inescapable Consequence of Mach’s Principle

#### 3.3. Evidence of the Presence of Fields in the Absence of ${T}^{ik}$

#### 3.4. A New Vision of Gravity in the Framework of GR: Spacetime Becomes a Physical Entity

#### 3.5. Equivalence Principle in the New Perspective

## 4. A Closer Look at the Conventional Four-Dimensional Formulation of Matter

#### 4.1. Problems with ${T}^{ik}$

## 5. Successes of the Novel Gravity Formulation

#### 5.1. Observational Support for the New Paradigm

#### 5.2. Different Pieces Fit Together

#### 5.3. Geometrization of Electromagnetism in the New Paradigm

## 6. Summary and Conclusions: What Next?

- It should explain the observed flat rotation curves of galaxies without requiring the ad-hoc dark matter.
- The net field in a homogeneous and isotropic background must be vanishing.

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Luminosity distance in the new model (continuous curve) is compared with that in the Λ CDM concordance model ${\Omega}_{\mathrm{m}}=1-{\Omega}_{\Lambda}=0.3$ (broken curve). Distances shown on the vertical axis are measured in units of $c{H}_{0}^{-1}$. The two models significantly depart for $z\phantom{\rule{0.166667em}{0ex}}\gtrsim $ 1.3.

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Vishwakarma, R.G.
Einstein and Beyond: A Critical Perspective on General Relativity. *Universe* **2016**, *2*, 11.
https://doi.org/10.3390/universe2020011

**AMA Style**

Vishwakarma RG.
Einstein and Beyond: A Critical Perspective on General Relativity. *Universe*. 2016; 2(2):11.
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Vishwakarma, Ram Gopal.
2016. "Einstein and Beyond: A Critical Perspective on General Relativity" *Universe* 2, no. 2: 11.
https://doi.org/10.3390/universe2020011