SKU: 6742059893

Interact Gravitation, Electromagnetic, Neutrino & Other Wave

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Description

Interact Gravitation, Electromagnetic, Neutrino & Other WaveThis book is devoted to researchers who would like to investigate interactions among gravitational waves and matter fields beyond linear order, including the phenomena of memory effects, gravitational Faraday rotation, soft theorems, and formations of spacetime singularities due to the mutual focus of gravitational waves. Readers only require a basic understanding of general relativity to understand the materials. The book starts with an overview on

This book is devoted to researchers who would like to investigate interactions among gravitational waves and matter fields beyond linear order, including the phenomena of memory effects, gravitational Faraday rotation, soft theorems, and formations of spacetime singularities due to the mutual focus of gravitational waves. Readers only require a basic understanding of general relativity to understand the materials.

The book starts with an overview on the fundamentals of the Newman-Penrose formalism and a brief introduction to distribution theory, with which the author systematically develops a mathematical description of spacetimes of colliding plane waves. Then, the author presents a frame-independent definition of polarization of a plane gravitational wave in a curved spacetime, studies in detail the gravitational Faraday rotation of two plane gravitational waves, and shows that each of them can serve as a medium to the other precisely due to their nonlinear interactions. Exact solutions are also presented, which represent a variety of models including the collisions of two plane gravitational waves and the collisions of a plane gravitational wave with a dust shell, a massless scalar wave, an electromagnetic wave, or a neutrino wave. The formation of spacetime singularities due to nonlinear interactions and the effects of gravitational wave polarization on the nature of singularities are also explored.

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SKU: 6742059893

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4.1 ★★★★★
Based on 8 reviews
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LC
Whiting, US
★★★★★ 5
LOVE THEM!!
Size: Small, Color: (001) Black / Black / Castlerock
LOVE! These socks are so comfortable! I wear a 5 in women's and a 3 in big kid shoes. The small fit me perfectly. I see where some say they run small but I can't say that was an issue for me. They are "snug" but thats what you want with a no show sock. I feel they have support vs the ones i used to buy at Walmart. They are very soft! I am actually buying more today and throwing my other ones in the trash!
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Reviewed in the United States on February 18, 2026
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Verified Purchase
Lucy Mejia
Natrona Heights, US
★★★★★ 5
So will not write down your foot
Size: Medium, Color: (001) Black / Black / Castlerock
I love these socks. They have a little bit of gel on the top of the heel for support in your tennis shoes and so your socks don’t write down. Very good quality.
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Reviewed in the United States on May 6, 2026
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Verified Purchase
Twins9
Dallas, US
★★★★★ 5
Comfy and Stay Put
Size: Medium, Color: (002) Black / Black / Halo Gray
These socks are honestly great. They’re super thin and light, so once you have them on, you kind of forget they’re even there. No bulky feeling in your shoes at all. The best part is they actually stay on. I hate no-show socks that slide down after five minutes, and these don’t do that. The little grip on the heel really works, so you’re not constantly adjusting them all day. They’re breathable too, which is nice if your feet run warm. They dry fast and don’t get that gross sweaty feeling. And there’s no annoying seam on the toe, so nothing rubs or feels uncomfortable. Basically, they’re just comfy, stay put, and don’t cause problems — which is all I want from socks.
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Reviewed in the United States on January 16, 2026
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swwkennyg
Alexandria, US
★★★★★ 5
Perfect sucks
Size: Medium, Color: (001) Black / Black / Castlerock
Wonderful socks . The weight is perfect !! These do not slip when in a shoe they stay out !!
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Reviewed in the United States on April 14, 2026
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Monica Alzate
Waukegan, US
★★★★★ 4
Amazing but quality changed
Size: Large, Color: (002) Black / Black / Halo Gray
Love these socks so much, been buying them for about 4 years now!! Not giving them 5 stars anymore because the quality is different and not as good, durable and thick as before.
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Reviewed in the United States on July 10, 2025

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