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1.When they travel to the watery planet, they say that 1 hour on this planet is 7 yrs om earth. How is this possible? Is the planet moving at a speed close to c? Or does strong gravitational field influence time? Sure. This is gravitational time dilation. It's due to the gravitational field of the black hole. You can calculate it using $$\frac{d ... 3 I tink your question is mostly answered by the answers to the question Universe being flat and why we can't see or access the space "behind" our universe plane?. The rubber sheet analogy gives the impression that there is an extra dimension in which spacetime is curved. Curvature in an extra dimension is called extrinsic curvature. However in ... 2 Have a look at my answer to How to explain centripetal force in terms or relativity because much of the discussion there is relevant. Consider what we mean by a tidal force. Suppose you're floating around in space and you arrange a number of marbles around you so they lie on the surface of a perfect sphere. Now monitor the shape of the surface marked out by ... 2 You're considering this in the noninertial frame of the earth, which makes it more confusing. In GR, we consider free-falling frames of reference to be the inertial frames. In such a frame, the ball's center of mass follows an inertial path, which looks like a straight line in spacetime. Meanwhile, the spot painted on the ball follows a parallel path ... 2 Eddington–Finkelstein coordinates use the same position coordinates as Schwarzschild coordinates, only the time coordinate is transformed, so first consider how to define Schwarzschild coordinates in a physical way. This pdf explains a way of defining the position coordinates in section 9.1.1: • We may assign a practical definition to the radial ... 2 Quite a philosophical approach. There is still the reliance on our four other senses in order to make sense of our physical world, however the same approach can be imply to those senses also with the delay in neurological impulses. One must also take into account, as you would call it, the in between frames of other people's perceptions, as well as those ... 2 General covariance basically means you can change your coordinate system arbitrarily and express the laws of physics in the new coordinates. Because of this freedom, the relationship between coordinate distances, angles, etc. and physical distances, angles, etc. is variable and is expressed by the metric. So the quoted statement is basically saying that ... 2 I'm hardly a GR expert, so if you want a more technical analysis I'm sure others will be able to give you one. However, the answer to your apparent questions is fairly straight forward. It is not the curvature of space or the curvature of time that causes accelerations, it is the curvature of space-time. We live in a four dimensional universe (ignoring ... 2 In a certain sense (regime) acceleration is caused by the curvature of time more than the curvature of space. Actually, the curvature is of the spacetime so that, making rigid distinctions has no much sense. However, if you consider the motion of a particle free falling in a region of spacetime, the equation of its story is the geodesical one: ... 2 The singularity comes from the scale factor a(t):$$ds^2 = -dt^2 + [a(t)]^2 ( dr^2 + r^2 d \Omega^2)$$By solving the Friedmann equations for the scale factor we know that:$$a(t) = a_0 t^{\lambda}$$where \lambda is some positive number that depends on the matter-radiation ratio of the universe. At t=0 the scale factor becomes a(0)=0. So at ... 1 Wald is a first rate relativist, and as such he is phrasing the concept of general covariance in terms of purely geometrical quantities, rather than resorting to the somewhat imprecise notion of coordinate transformations. In the discussion on pg. 57, he goes on to give an example of what it means to violate the principle of general covariance. In his ... 1 Fortunately for experiments in physics we have better proxies than the accuracies of our five senses. We have detectors and computers and .... With these tools a theory of how the universe is made has been developed, from elementary particles with the theory of quantum mechanics building up the observables around us, to the astrophysical models that fit ... 1 In special relativity, mass / energy has no influence on spacetime. However, in general relativity, the curvature of spacetime is directly related to energy, or equivalently, mass. The Einstein field equation$$R_{\mu \nu} - {1 \over 2}g_{\mu \nu}\,R + g_{\mu \nu} \Lambda = {8 \pi G \over c^4} T_{\mu \nu}$$includes the stress-energy tensor, which ... 1 E=m*c**2 is not the defining equation of relativity. The theory is called special relativity and the equation is a derived part of the results of the theory. It is the result of Lorenz transformations on moving systems, which do take care of space and time in addition to energy. 1 Is space-time warped around the spaceship? No, not measurably. The time dilation effect does not arise from any curvature of spacetime. Space-time is warped by gravity (the stronger the gravitational field the slower time goes). The parenthetical statement is not really a correct description of what spacetime curvature is. Spacetime curvature is ... 1 That's the definition of the dot product in Minkowski space-time. To be clear, any space-time is endowed with a metric. Standard {\mathbb R}^3 that you may be familiar with has a metric \delta_{ij} = \text{diag}(1,1,1), i=1,2,3. Given two vector \vec{v} = (v^1,v^2,v^3) or v^i for short and similarly w^i, the dot product is defined as$$ \vec{v} ...